Finite Math Examples

Solve for z |1+iz|=|1-iz|
Step 1
Rewrite the equation as .
Step 2
Rewrite the absolute value equation as four equations without absolute value bars.
Step 3
After simplifying, there are only two unique equations to be solved.
Step 4
Solve for .
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Step 4.1
Move all terms containing to the left side of the equation.
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Step 4.1.1
Subtract from both sides of the equation.
Step 4.1.2
Subtract from .
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
Subtract from .
Step 4.3
Divide each term in by and simplify.
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Step 4.3.1
Divide each term in by .
Step 4.3.2
Simplify the left side.
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Step 4.3.2.1
Cancel the common factor of .
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Step 4.3.2.1.1
Cancel the common factor.
Step 4.3.2.1.2
Rewrite the expression.
Step 4.3.2.2
Cancel the common factor of .
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Step 4.3.2.2.1
Cancel the common factor.
Step 4.3.2.2.2
Divide by .
Step 4.3.3
Simplify the right side.
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Step 4.3.3.1
Cancel the common factor of and .
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Step 4.3.3.1.1
Factor out of .
Step 4.3.3.1.2
Cancel the common factors.
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Step 4.3.3.1.2.1
Factor out of .
Step 4.3.3.1.2.2
Cancel the common factor.
Step 4.3.3.1.2.3
Rewrite the expression.
Step 4.3.3.2
Multiply the numerator and denominator of by the conjugate of to make the denominator real.
Step 4.3.3.3
Multiply.
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Step 4.3.3.3.1
Combine.
Step 4.3.3.3.2
Multiply by .
Step 4.3.3.3.3
Simplify the denominator.
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Step 4.3.3.3.3.1
Add parentheses.
Step 4.3.3.3.3.2
Raise to the power of .
Step 4.3.3.3.3.3
Raise to the power of .
Step 4.3.3.3.3.4
Use the power rule to combine exponents.
Step 4.3.3.3.3.5
Add and .
Step 4.3.3.3.3.6
Rewrite as .
Step 4.3.3.4
Multiply by .
Step 4.3.3.5
Divide by .
Step 5
Solve for .
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Step 5.1
Simplify .
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Step 5.1.1
Rewrite.
Step 5.1.2
Simplify by adding zeros.
Step 5.1.3
Apply the distributive property.
Step 5.1.4
Multiply by .
Step 5.2
Move all terms containing to the left side of the equation.
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Step 5.2.1
Add to both sides of the equation.
Step 5.2.2
Combine the opposite terms in .
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Step 5.2.2.1
Add and .
Step 5.2.2.2
Add and .
Step 5.3
Since , there are no solutions.
No solution
No solution
Step 6
List all of the solutions.
Step 7
Exclude the solutions that do not make true.