Trigonometry Examples

Rationalize the Denominator ( square root of 5+i square root of 15)/(5 square root of 15+5i square root of 5)
Step 1
Multiply by .
Step 2
Simplify terms.
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Step 2.1
Multiply by .
Step 2.2
Expand the denominator using the FOIL method.
Step 2.3
Simplify.
Step 2.4
Cancel the common factor of and .
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Step 2.4.1
Factor out of .
Step 2.4.2
Cancel the common factors.
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Step 2.4.2.1
Factor out of .
Step 2.4.2.2
Cancel the common factor.
Step 2.4.2.3
Rewrite the expression.
Step 3
Expand using the FOIL Method.
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Step 3.1
Apply the distributive property.
Step 3.2
Apply the distributive property.
Step 3.3
Apply the distributive property.
Step 4
Simplify and combine like terms.
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Step 4.1
Simplify each term.
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Step 4.1.1
Combine using the product rule for radicals.
Step 4.1.2
Multiply by .
Step 4.1.3
Rewrite as .
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Step 4.1.3.1
Factor out of .
Step 4.1.3.2
Rewrite as .
Step 4.1.4
Pull terms out from under the radical.
Step 4.1.5
Multiply .
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Step 4.1.5.1
Raise to the power of .
Step 4.1.5.2
Raise to the power of .
Step 4.1.5.3
Use the power rule to combine exponents.
Step 4.1.5.4
Add and .
Step 4.1.6
Rewrite as .
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Step 4.1.6.1
Use to rewrite as .
Step 4.1.6.2
Apply the power rule and multiply exponents, .
Step 4.1.6.3
Combine and .
Step 4.1.6.4
Cancel the common factor of .
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Step 4.1.6.4.1
Cancel the common factor.
Step 4.1.6.4.2
Rewrite the expression.
Step 4.1.6.5
Evaluate the exponent.
Step 4.1.7
Multiply by .
Step 4.1.8
Multiply .
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Step 4.1.8.1
Raise to the power of .
Step 4.1.8.2
Raise to the power of .
Step 4.1.8.3
Use the power rule to combine exponents.
Step 4.1.8.4
Add and .
Step 4.1.9
Rewrite as .
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Step 4.1.9.1
Use to rewrite as .
Step 4.1.9.2
Apply the power rule and multiply exponents, .
Step 4.1.9.3
Combine and .
Step 4.1.9.4
Cancel the common factor of .
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Step 4.1.9.4.1
Cancel the common factor.
Step 4.1.9.4.2
Rewrite the expression.
Step 4.1.9.5
Evaluate the exponent.
Step 4.1.10
Move to the left of .
Step 4.1.11
Multiply .
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Step 4.1.11.1
Raise to the power of .
Step 4.1.11.2
Raise to the power of .
Step 4.1.11.3
Use the power rule to combine exponents.
Step 4.1.11.4
Add and .
Step 4.1.11.5
Combine using the product rule for radicals.
Step 4.1.11.6
Multiply by .
Step 4.1.12
Rewrite as .
Step 4.1.13
Multiply by .
Step 4.1.14
Multiply by .
Step 4.1.15
Rewrite as .
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Step 4.1.15.1
Factor out of .
Step 4.1.15.2
Rewrite as .
Step 4.1.16
Pull terms out from under the radical.
Step 4.2
Add and .
Step 4.3
Add and .
Step 5
Reorder and .
Step 6
Cancel the common factor of and .
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Step 6.1
Factor out of .
Step 6.2
Factor out of .
Step 6.3
Factor out of .
Step 6.4
Cancel the common factors.
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Step 6.4.1
Factor out of .
Step 6.4.2
Cancel the common factor.
Step 6.4.3
Rewrite the expression.