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Popular >

simplify (e^{iθ}+e^{-iθ})^4

Solution

simplify

(e^{i θ} + e^{- i θ})^{4}

Solution

16 cos^{4} (θ)

Solution steps

(e^{i θ} + e^{- i θ})^{4}

e^{i θ} = cos (θ) + i sin (θ)

e^{- i θ} = cos (θ) - i sin (θ)

= (cos (θ) + i sin (θ) + cos (θ) - i sin (θ))^{4}

Simplify

cos (θ) + sin (θ) i + cos (θ) - i sin (θ) : 2 cos (θ)

= (2 cos (θ))^{4}

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

= 2^{4} cos^{4} (θ)

2^{4} = 16

= 16 cos^{4} (θ)

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Frequently Asked Questions (FAQ)

What is (e^{iθ}+e^{-iθ})^4 ?
The solution to (e^{iθ}+e^{-iθ})^4 is 16cos^4(θ)