Finite Math Examples

Solve for x ((1+i)^2)/((1-i)^2)+2/(x+iy)=2+2i
Step 1
Move all terms not containing to the right side of the equation.
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Step 1.1
Subtract from both sides of the equation.
Step 1.2
Simplify each term.
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Step 1.2.1
Rewrite as .
Step 1.2.2
Expand using the FOIL Method.
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Step 1.2.2.1
Apply the distributive property.
Step 1.2.2.2
Apply the distributive property.
Step 1.2.2.3
Apply the distributive property.
Step 1.2.3
Simplify and combine like terms.
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Step 1.2.3.1
Simplify each term.
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Step 1.2.3.1.1
Multiply by .
Step 1.2.3.1.2
Multiply by .
Step 1.2.3.1.3
Multiply by .
Step 1.2.3.1.4
Multiply .
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Step 1.2.3.1.4.1
Raise to the power of .
Step 1.2.3.1.4.2
Raise to the power of .
Step 1.2.3.1.4.3
Use the power rule to combine exponents.
Step 1.2.3.1.4.4
Add and .
Step 1.2.3.1.5
Rewrite as .
Step 1.2.3.2
Subtract from .
Step 1.2.3.3
Add and .
Step 1.2.3.4
Add and .
Step 1.2.4
Rewrite as .
Step 1.2.5
Expand using the FOIL Method.
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Step 1.2.5.1
Apply the distributive property.
Step 1.2.5.2
Apply the distributive property.
Step 1.2.5.3
Apply the distributive property.
Step 1.2.6
Simplify and combine like terms.
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Step 1.2.6.1
Simplify each term.
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Step 1.2.6.1.1
Multiply by .
Step 1.2.6.1.2
Multiply by .
Step 1.2.6.1.3
Multiply by .
Step 1.2.6.1.4
Multiply .
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Step 1.2.6.1.4.1
Multiply by .
Step 1.2.6.1.4.2
Raise to the power of .
Step 1.2.6.1.4.3
Raise to the power of .
Step 1.2.6.1.4.4
Use the power rule to combine exponents.
Step 1.2.6.1.4.5
Add and .
Step 1.2.6.1.4.6
Multiply by .
Step 1.2.6.1.5
Rewrite as .
Step 1.2.6.2
Subtract from .
Step 1.2.6.3
Subtract from .
Step 1.2.6.4
Subtract from .
Step 1.2.7
Cancel the common factor of and .
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Step 1.2.7.1
Factor out of .
Step 1.2.7.2
Cancel the common factors.
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Step 1.2.7.2.1
Factor out of .
Step 1.2.7.2.2
Cancel the common factor.
Step 1.2.7.2.3
Rewrite the expression.
Step 1.2.8
Cancel the common factor of .
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Step 1.2.8.1
Cancel the common factor.
Step 1.2.8.2
Rewrite the expression.
Step 1.2.8.3
Move the negative one from the denominator of .
Step 1.2.9
Multiply .
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Step 1.2.9.1
Multiply by .
Step 1.2.9.2
Multiply by .
Step 1.3
Add and .
Step 2
Find the LCD of the terms in the equation.
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Step 2.1
Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.
Step 2.2
Remove parentheses.
Step 2.3
The LCM of one and any expression is the expression.
Step 3
Multiply each term in by to eliminate the fractions.
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Step 3.1
Multiply each term in by .
Step 3.2
Simplify the left side.
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Step 3.2.1
Cancel the common factor of .
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Step 3.2.1.1
Cancel the common factor.
Step 3.2.1.2
Rewrite the expression.
Step 3.3
Simplify the right side.
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Step 3.3.1
Simplify each term.
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Step 3.3.1.1
Apply the distributive property.
Step 3.3.1.2
Apply the distributive property.
Step 3.3.1.3
Multiply .
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Step 3.3.1.3.1
Raise to the power of .
Step 3.3.1.3.2
Raise to the power of .
Step 3.3.1.3.3
Use the power rule to combine exponents.
Step 3.3.1.3.4
Add and .
Step 3.3.1.4
Simplify each term.
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Step 3.3.1.4.1
Rewrite as .
Step 3.3.1.4.2
Multiply by .
Step 4
Solve the equation.
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Step 4.1
Rewrite the equation as .
Step 4.2
Move all terms not containing to the right side of the equation.
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Step 4.2.1
Subtract from both sides of the equation.
Step 4.2.2
Add to both sides of the equation.
Step 4.3
Factor out of .
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Step 4.3.1
Factor out of .
Step 4.3.2
Factor out of .
Step 4.3.3
Factor out of .
Step 4.4
Divide each term in by and simplify.
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Step 4.4.1
Divide each term in by .
Step 4.4.2
Simplify the left side.
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Step 4.4.2.1
Cancel the common factor of .
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Step 4.4.2.1.1
Cancel the common factor.
Step 4.4.2.1.2
Divide by .
Step 4.4.3
Simplify the right side.
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Step 4.4.3.1
Simplify each term.
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Step 4.4.3.1.1
Multiply the numerator and denominator of by the conjugate of to make the denominator real.
Step 4.4.3.1.2
Multiply.
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Step 4.4.3.1.2.1
Combine.
Step 4.4.3.1.2.2
Simplify the numerator.
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Step 4.4.3.1.2.2.1
Apply the distributive property.
Step 4.4.3.1.2.2.2
Multiply by .
Step 4.4.3.1.2.2.3
Multiply by .
Step 4.4.3.1.2.3
Simplify the denominator.
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Step 4.4.3.1.2.3.1
Expand using the FOIL Method.
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Step 4.4.3.1.2.3.1.1
Apply the distributive property.
Step 4.4.3.1.2.3.1.2
Apply the distributive property.
Step 4.4.3.1.2.3.1.3
Apply the distributive property.
Step 4.4.3.1.2.3.2
Simplify.
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Step 4.4.3.1.2.3.2.1
Multiply by .
Step 4.4.3.1.2.3.2.2
Multiply by .
Step 4.4.3.1.2.3.2.3
Multiply by .
Step 4.4.3.1.2.3.2.4
Multiply by .
Step 4.4.3.1.2.3.2.5
Raise to the power of .
Step 4.4.3.1.2.3.2.6
Raise to the power of .
Step 4.4.3.1.2.3.2.7
Use the power rule to combine exponents.
Step 4.4.3.1.2.3.2.8
Add and .
Step 4.4.3.1.2.3.2.9
Add and .
Step 4.4.3.1.2.3.2.10
Add and .
Step 4.4.3.1.2.3.3
Simplify each term.
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Step 4.4.3.1.2.3.3.1
Rewrite as .
Step 4.4.3.1.2.3.3.2
Multiply by .
Step 4.4.3.1.2.3.4
Add and .
Step 4.4.3.1.3
Split the fraction into two fractions.
Step 4.4.3.1.4
Move the negative in front of the fraction.
Step 4.4.3.1.5
Multiply the numerator and denominator of by the conjugate of to make the denominator real.
Step 4.4.3.1.6
Multiply.
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Step 4.4.3.1.6.1
Combine.
Step 4.4.3.1.6.2
Simplify the numerator.
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Step 4.4.3.1.6.2.1
Apply the distributive property.
Step 4.4.3.1.6.2.2
Multiply by .
Step 4.4.3.1.6.2.3
Multiply .
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Step 4.4.3.1.6.2.3.1
Multiply by .
Step 4.4.3.1.6.2.3.2
Raise to the power of .
Step 4.4.3.1.6.2.3.3
Raise to the power of .
Step 4.4.3.1.6.2.3.4
Use the power rule to combine exponents.
Step 4.4.3.1.6.2.3.5
Add and .
Step 4.4.3.1.6.2.4
Simplify each term.
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Step 4.4.3.1.6.2.4.1
Rewrite as .
Step 4.4.3.1.6.2.4.2
Multiply by .
Step 4.4.3.1.6.3
Simplify the denominator.
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Step 4.4.3.1.6.3.1
Expand using the FOIL Method.
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Step 4.4.3.1.6.3.1.1
Apply the distributive property.
Step 4.4.3.1.6.3.1.2
Apply the distributive property.
Step 4.4.3.1.6.3.1.3
Apply the distributive property.
Step 4.4.3.1.6.3.2
Simplify.
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Step 4.4.3.1.6.3.2.1
Multiply by .
Step 4.4.3.1.6.3.2.2
Multiply by .
Step 4.4.3.1.6.3.2.3
Multiply by .
Step 4.4.3.1.6.3.2.4
Multiply by .
Step 4.4.3.1.6.3.2.5
Raise to the power of .
Step 4.4.3.1.6.3.2.6
Raise to the power of .
Step 4.4.3.1.6.3.2.7
Use the power rule to combine exponents.
Step 4.4.3.1.6.3.2.8
Add and .
Step 4.4.3.1.6.3.2.9
Add and .
Step 4.4.3.1.6.3.2.10
Add and .
Step 4.4.3.1.6.3.3
Simplify each term.
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Step 4.4.3.1.6.3.3.1
Rewrite as .
Step 4.4.3.1.6.3.3.2
Multiply by .
Step 4.4.3.1.6.3.4
Add and .
Step 4.4.3.1.7
Factor out of .
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Step 4.4.3.1.7.1
Factor out of .
Step 4.4.3.1.7.2
Factor out of .
Step 4.4.3.1.7.3
Factor out of .
Step 4.4.3.1.8
Multiply the numerator and denominator of by the conjugate of to make the denominator real.
Step 4.4.3.1.9
Multiply.
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Step 4.4.3.1.9.1
Combine.
Step 4.4.3.1.9.2
Simplify the numerator.
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Step 4.4.3.1.9.2.1
Apply the distributive property.
Step 4.4.3.1.9.2.2
Multiply by .
Step 4.4.3.1.9.2.3
Multiply by .
Step 4.4.3.1.9.3
Simplify the denominator.
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Step 4.4.3.1.9.3.1
Expand using the FOIL Method.
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Step 4.4.3.1.9.3.1.1
Apply the distributive property.
Step 4.4.3.1.9.3.1.2
Apply the distributive property.
Step 4.4.3.1.9.3.1.3
Apply the distributive property.
Step 4.4.3.1.9.3.2
Simplify.
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Step 4.4.3.1.9.3.2.1
Multiply by .
Step 4.4.3.1.9.3.2.2
Multiply by .
Step 4.4.3.1.9.3.2.3
Multiply by .
Step 4.4.3.1.9.3.2.4
Multiply by .
Step 4.4.3.1.9.3.2.5
Raise to the power of .
Step 4.4.3.1.9.3.2.6
Raise to the power of .
Step 4.4.3.1.9.3.2.7
Use the power rule to combine exponents.
Step 4.4.3.1.9.3.2.8
Add and .
Step 4.4.3.1.9.3.2.9
Add and .
Step 4.4.3.1.9.3.2.10
Add and .
Step 4.4.3.1.9.3.3
Simplify each term.
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Step 4.4.3.1.9.3.3.1
Rewrite as .
Step 4.4.3.1.9.3.3.2
Multiply by .
Step 4.4.3.1.9.3.4
Add and .
Step 4.4.3.1.10
Factor out of .
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Step 4.4.3.1.10.1
Factor out of .
Step 4.4.3.1.10.2
Factor out of .
Step 4.4.3.1.10.3
Factor out of .
Step 4.4.3.2
Combine the numerators over the common denominator.
Step 4.4.3.3
Simplify each term.
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Step 4.4.3.3.1
Apply the distributive property.
Step 4.4.3.3.2
Multiply by .
Step 4.4.3.3.3
Multiply by .
Step 4.4.3.3.4
Apply the distributive property.
Step 4.4.3.3.5
Multiply by .
Step 4.4.3.3.6
Multiply by .
Step 4.4.3.4
Simplify terms.
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Step 4.4.3.4.1
Combine the opposite terms in .
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Step 4.4.3.4.1.1
Add and .
Step 4.4.3.4.1.2
Add and .
Step 4.4.3.4.2
Subtract from .
Step 4.4.3.4.3
Reorder terms.
Step 4.4.3.4.4
Factor out of .
Step 4.4.3.4.5
Rewrite as .
Step 4.4.3.4.6
Factor out of .
Step 4.4.3.4.7
Factor out of .
Step 4.4.3.4.8
Factor out of .
Step 4.4.3.4.9
Simplify the expression.
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Step 4.4.3.4.9.1
Rewrite as .
Step 4.4.3.4.9.2
Move the negative in front of the fraction.