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Popular >

simplify (e^{iz}+e^{-iz})^2

Solution

simplify

(e^{i z} + e^{- i z})^{2}

Solution

4 cos^{2} (z)

Solution steps

(e^{i z} + e^{- i z})^{2}

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

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

= (cos (z) + i sin (z) + cos (z) - i sin (z))^{2}

Simplify

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

= (2 cos (z))^{2}

Apply exponent rule:

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

= 2^{2} cos^{2} (z)

2^{2} = 4

= 4 cos^{2} (z)

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Frequently Asked Questions (FAQ)

What is (e^{iz}+e^{-iz})^2 ?
The solution to (e^{iz}+e^{-iz})^2 is 4cos^2(z)