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Popular >

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

Solution

simplify

(e^{ia} + e^{- ia})^{2}

Solution

4 cos^{2} (a)

Solution steps

(e^{ia} + e^{- ia})^{2}

e^{ia} = cos (a) + i sin (a)

e^{- ia} = cos (a) - i sin (a)

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

Simplify

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

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

Apply exponent rule:

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

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

2^{2} = 4

= 4 cos^{2} (a)

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Frequently Asked Questions (FAQ)

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