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Popular >

simplify (e^{ix}+e^{-ix})^4

Solution

simplify

(e^{i x} + e^{- i x})^{4}

Solution

16 cos^{4} (x)

Solution steps

(e^{i x} + e^{- i x})^{4}

e^{i x} = cos (x) + i sin (x)

e^{- i x} = cos (x) - i sin (x)

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

Simplify

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

= (2 cos (x))^{4}

Apply exponent rule:

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

= 2^{4} cos^{4} (x)

2^{4} = 16

= 16 cos^{4} (x)

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Frequently Asked Questions (FAQ)

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