Basic Math Examples

Solve for z |(i+2 square root of 2)*z|=6
Step 1
Remove the absolute value term. This creates a on the right side of the equation because .
Step 2
The complete solution is the result of both the positive and negative portions of the solution.
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Step 2.1
First, use the positive value of the to find the first solution.
Step 2.2
Divide each term in by and simplify.
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Step 2.2.1
Divide each term in by .
Step 2.2.2
Simplify the left side.
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Step 2.2.2.1
Cancel the common factor of .
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Step 2.2.2.1.1
Cancel the common factor.
Step 2.2.2.1.2
Divide by .
Step 2.2.3
Simplify the right side.
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Step 2.2.3.1
Multiply the numerator and denominator of by the conjugate of to make the denominator real.
Step 2.2.3.2
Multiply.
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Step 2.2.3.2.1
Combine.
Step 2.2.3.2.2
Simplify the numerator.
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Step 2.2.3.2.2.1
Apply the distributive property.
Step 2.2.3.2.2.2
Multiply by .
Step 2.2.3.2.2.3
Multiply by .
Step 2.2.3.2.3
Simplify the denominator.
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Step 2.2.3.2.3.1
Expand using the FOIL Method.
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Step 2.2.3.2.3.1.1
Apply the distributive property.
Step 2.2.3.2.3.1.2
Apply the distributive property.
Step 2.2.3.2.3.1.3
Apply the distributive property.
Step 2.2.3.2.3.2
Simplify.
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Step 2.2.3.2.3.2.1
Multiply by .
Step 2.2.3.2.3.2.2
Multiply by .
Step 2.2.3.2.3.2.3
Multiply by .
Step 2.2.3.2.3.2.4
Multiply by .
Step 2.2.3.2.3.2.5
Raise to the power of .
Step 2.2.3.2.3.2.6
Raise to the power of .
Step 2.2.3.2.3.2.7
Use the power rule to combine exponents.
Step 2.2.3.2.3.2.8
Add and .
Step 2.2.3.2.3.2.9
Add and .
Step 2.2.3.2.3.3
Simplify each term.
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Step 2.2.3.2.3.3.1
Multiply by .
Step 2.2.3.2.3.3.2
Rewrite as .
Step 2.2.3.2.3.3.3
Multiply by .
Step 2.2.3.2.3.4
Add and .
Step 2.2.3.2.3.5
Add and .
Step 2.2.3.3
Rewrite as .
Step 2.2.3.4
Factor out of .
Step 2.2.3.5
Factor out of .
Step 2.2.3.6
Factor out of .
Step 2.2.3.7
Separate fractions.
Step 2.2.3.8
Simplify the expression.
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Step 2.2.3.8.1
Divide by .
Step 2.2.3.8.2
Divide by .
Step 2.2.3.9
Apply the distributive property.
Step 2.2.3.10
Multiply.
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Step 2.2.3.10.1
Multiply by .
Step 2.2.3.10.2
Multiply by .
Step 2.3
Next, use the negative value of the to find the second solution.
Step 2.4
Divide each term in by and simplify.
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Step 2.4.1
Divide each term in by .
Step 2.4.2
Simplify the left side.
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Step 2.4.2.1
Cancel the common factor of .
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Step 2.4.2.1.1
Cancel the common factor.
Step 2.4.2.1.2
Divide by .
Step 2.4.3
Simplify the right side.
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Step 2.4.3.1
Multiply the numerator and denominator of by the conjugate of to make the denominator real.
Step 2.4.3.2
Multiply.
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Step 2.4.3.2.1
Combine.
Step 2.4.3.2.2
Simplify the numerator.
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Step 2.4.3.2.2.1
Apply the distributive property.
Step 2.4.3.2.2.2
Multiply by .
Step 2.4.3.2.2.3
Multiply by .
Step 2.4.3.2.3
Simplify the denominator.
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Step 2.4.3.2.3.1
Expand using the FOIL Method.
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Step 2.4.3.2.3.1.1
Apply the distributive property.
Step 2.4.3.2.3.1.2
Apply the distributive property.
Step 2.4.3.2.3.1.3
Apply the distributive property.
Step 2.4.3.2.3.2
Simplify.
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Step 2.4.3.2.3.2.1
Multiply by .
Step 2.4.3.2.3.2.2
Multiply by .
Step 2.4.3.2.3.2.3
Multiply by .
Step 2.4.3.2.3.2.4
Multiply by .
Step 2.4.3.2.3.2.5
Raise to the power of .
Step 2.4.3.2.3.2.6
Raise to the power of .
Step 2.4.3.2.3.2.7
Use the power rule to combine exponents.
Step 2.4.3.2.3.2.8
Add and .
Step 2.4.3.2.3.2.9
Add and .
Step 2.4.3.2.3.3
Simplify each term.
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Step 2.4.3.2.3.3.1
Multiply by .
Step 2.4.3.2.3.3.2
Rewrite as .
Step 2.4.3.2.3.3.3
Multiply by .
Step 2.4.3.2.3.4
Add and .
Step 2.4.3.2.3.5
Add and .
Step 2.4.3.3
Rewrite as .
Step 2.4.3.4
Factor out of .
Step 2.4.3.5
Factor out of .
Step 2.4.3.6
Factor out of .
Step 2.4.3.7
Separate fractions.
Step 2.4.3.8
Simplify the expression.
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Step 2.4.3.8.1
Divide by .
Step 2.4.3.8.2
Divide by .
Step 2.4.3.9
Apply the distributive property.
Step 2.4.3.10
Multiply.
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Step 2.4.3.10.1
Multiply by .
Step 2.4.3.10.2
Multiply by .
Step 2.5
The complete solution is the result of both the positive and negative portions of the solution.