Finite Math Examples

Evaluate ((2i)^2)/(4-(2i))
Step 1
Multiply the numerator and denominator of by the conjugate of to make the denominator real.
Step 2
Multiply.
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Step 2.1
Combine.
Step 2.2
Simplify the numerator.
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Step 2.2.1
Apply the product rule to .
Step 2.2.2
Raise to the power of .
Step 2.2.3
Rewrite as .
Step 2.2.4
Multiply by .
Step 2.2.5
Apply the distributive property.
Step 2.2.6
Multiply by .
Step 2.2.7
Multiply by .
Step 2.3
Simplify the denominator.
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Step 2.3.1
Expand using the FOIL Method.
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Step 2.3.1.1
Apply the distributive property.
Step 2.3.1.2
Apply the distributive property.
Step 2.3.1.3
Apply the distributive property.
Step 2.3.2
Simplify.
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Step 2.3.2.1
Multiply by .
Step 2.3.2.2
Multiply by .
Step 2.3.2.3
Multiply by .
Step 2.3.2.4
Multiply by .
Step 2.3.2.5
Raise to the power of .
Step 2.3.2.6
Raise to the power of .
Step 2.3.2.7
Use the power rule to combine exponents.
Step 2.3.2.8
Add and .
Step 2.3.2.9
Subtract from .
Step 2.3.2.10
Add and .
Step 2.3.3
Simplify each term.
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Step 2.3.3.1
Rewrite as .
Step 2.3.3.2
Multiply by .
Step 2.3.4
Add and .
Step 3
Cancel the common factor of and .
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Step 3.1
Factor out of .
Step 3.2
Factor out of .
Step 3.3
Factor out of .
Step 3.4
Cancel the common factors.
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Step 3.4.1
Factor out of .
Step 3.4.2
Cancel the common factor.
Step 3.4.3
Rewrite the expression.
Step 4
Split the fraction into two fractions.
Step 5
Simplify each term.
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Step 5.1
Move the negative in front of the fraction.
Step 5.2
Move the negative in front of the fraction.