Trigonometry Examples

Simplify (1- square root of 3i)^7
Step 1
Use the Binomial Theorem.
Step 2
Simplify terms.
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Step 2.1
Simplify each term.
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Step 2.1.1
One to any power is one.
Step 2.1.2
One to any power is one.
Step 2.1.3
Multiply by .
Step 2.1.4
Multiply by .
Step 2.1.5
One to any power is one.
Step 2.1.6
Multiply by .
Step 2.1.7
Use the power rule to distribute the exponent.
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Step 2.1.7.1
Apply the product rule to .
Step 2.1.7.2
Apply the product rule to .
Step 2.1.8
Raise to the power of .
Step 2.1.9
Multiply by .
Step 2.1.10
Rewrite as .
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Step 2.1.10.1
Use to rewrite as .
Step 2.1.10.2
Apply the power rule and multiply exponents, .
Step 2.1.10.3
Combine and .
Step 2.1.10.4
Cancel the common factor of .
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Step 2.1.10.4.1
Cancel the common factor.
Step 2.1.10.4.2
Rewrite the expression.
Step 2.1.10.5
Evaluate the exponent.
Step 2.1.11
Rewrite as .
Step 2.1.12
Multiply .
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Step 2.1.12.1
Multiply by .
Step 2.1.12.2
Multiply by .
Step 2.1.13
One to any power is one.
Step 2.1.14
Multiply by .
Step 2.1.15
Use the power rule to distribute the exponent.
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Step 2.1.15.1
Apply the product rule to .
Step 2.1.15.2
Apply the product rule to .
Step 2.1.16
Raise to the power of .
Step 2.1.17
Rewrite as .
Step 2.1.18
Raise to the power of .
Step 2.1.19
Rewrite as .
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Step 2.1.19.1
Factor out of .
Step 2.1.19.2
Rewrite as .
Step 2.1.20
Pull terms out from under the radical.
Step 2.1.21
Multiply by .
Step 2.1.22
Factor out .
Step 2.1.23
Rewrite as .
Step 2.1.24
Rewrite as .
Step 2.1.25
Multiply by .
Step 2.1.26
Multiply by .
Step 2.1.27
One to any power is one.
Step 2.1.28
Multiply by .
Step 2.1.29
Use the power rule to distribute the exponent.
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Step 2.1.29.1
Apply the product rule to .
Step 2.1.29.2
Apply the product rule to .
Step 2.1.30
Raise to the power of .
Step 2.1.31
Multiply by .
Step 2.1.32
Rewrite as .
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Step 2.1.32.1
Use to rewrite as .
Step 2.1.32.2
Apply the power rule and multiply exponents, .
Step 2.1.32.3
Combine and .
Step 2.1.32.4
Cancel the common factor of and .
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Step 2.1.32.4.1
Factor out of .
Step 2.1.32.4.2
Cancel the common factors.
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Step 2.1.32.4.2.1
Factor out of .
Step 2.1.32.4.2.2
Cancel the common factor.
Step 2.1.32.4.2.3
Rewrite the expression.
Step 2.1.32.4.2.4
Divide by .
Step 2.1.33
Raise to the power of .
Step 2.1.34
Rewrite as .
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Step 2.1.34.1
Rewrite as .
Step 2.1.34.2
Rewrite as .
Step 2.1.34.3
Raise to the power of .
Step 2.1.35
Multiply .
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Step 2.1.35.1
Multiply by .
Step 2.1.35.2
Multiply by .
Step 2.1.36
One to any power is one.
Step 2.1.37
Multiply by .
Step 2.1.38
Use the power rule to distribute the exponent.
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Step 2.1.38.1
Apply the product rule to .
Step 2.1.38.2
Apply the product rule to .
Step 2.1.39
Raise to the power of .
Step 2.1.40
Rewrite as .
Step 2.1.41
Raise to the power of .
Step 2.1.42
Rewrite as .
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Step 2.1.42.1
Factor out of .
Step 2.1.42.2
Rewrite as .
Step 2.1.43
Pull terms out from under the radical.
Step 2.1.44
Multiply by .
Step 2.1.45
Factor out .
Step 2.1.46
Rewrite as .
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Step 2.1.46.1
Rewrite as .
Step 2.1.46.2
Rewrite as .
Step 2.1.46.3
Raise to the power of .
Step 2.1.47
Multiply by .
Step 2.1.48
Multiply by .
Step 2.1.49
Multiply by .
Step 2.1.50
Use the power rule to distribute the exponent.
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Step 2.1.50.1
Apply the product rule to .
Step 2.1.50.2
Apply the product rule to .
Step 2.1.51
Raise to the power of .
Step 2.1.52
Multiply by .
Step 2.1.53
Rewrite as .
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Step 2.1.53.1
Use to rewrite as .
Step 2.1.53.2
Apply the power rule and multiply exponents, .
Step 2.1.53.3
Combine and .
Step 2.1.53.4
Cancel the common factor of and .
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Step 2.1.53.4.1
Factor out of .
Step 2.1.53.4.2
Cancel the common factors.
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Step 2.1.53.4.2.1
Factor out of .
Step 2.1.53.4.2.2
Cancel the common factor.
Step 2.1.53.4.2.3
Rewrite the expression.
Step 2.1.53.4.2.4
Divide by .
Step 2.1.54
Raise to the power of .
Step 2.1.55
Factor out .
Step 2.1.56
Rewrite as .
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Step 2.1.56.1
Rewrite as .
Step 2.1.56.2
Rewrite as .
Step 2.1.56.3
Raise to the power of .
Step 2.1.57
Multiply by .
Step 2.1.58
Rewrite as .
Step 2.1.59
Multiply .
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Step 2.1.59.1
Multiply by .
Step 2.1.59.2
Multiply by .
Step 2.1.60
Use the power rule to distribute the exponent.
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Step 2.1.60.1
Apply the product rule to .
Step 2.1.60.2
Apply the product rule to .
Step 2.1.61
Raise to the power of .
Step 2.1.62
Rewrite as .
Step 2.1.63
Raise to the power of .
Step 2.1.64
Rewrite as .
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Step 2.1.64.1
Factor out of .
Step 2.1.64.2
Rewrite as .
Step 2.1.65
Pull terms out from under the radical.
Step 2.1.66
Multiply by .
Step 2.1.67
Rewrite as .
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Step 2.1.67.1
Factor out .
Step 2.1.67.2
Factor out .
Step 2.1.68
Rewrite as .
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Step 2.1.68.1
Rewrite as .
Step 2.1.68.2
Rewrite as .
Step 2.1.68.3
Raise to the power of .
Step 2.1.69
Multiply by .
Step 2.1.70
Rewrite as .
Step 2.1.71
Rewrite as .
Step 2.1.72
Multiply by .
Step 2.2
Simplify by adding terms.
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Step 2.2.1
Subtract from .
Step 2.2.2
Add and .
Step 2.2.3
Subtract from .
Step 2.2.4
Add and .
Step 2.2.5
Simplify the expression.
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Step 2.2.5.1
Add and .
Step 2.2.5.2
Subtract from .
Step 2.2.5.3
Reorder and .