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Popular >

simplify (e^{i2t}+e^{-i2t})^2

Solution

simplify

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

Solution

4 cos^{2} (2 t)

Solution steps

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

e^{i 2 t} = cos (2 t) + i sin (2 t)

e^{- i 2 t} = cos (2 t) - i sin (2 t)

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

Simplify

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

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

Apply exponent rule:

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

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

2^{2} = 4

= 4 cos^{2} (2 t)

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Frequently Asked Questions (FAQ)

What is (e^{i2t}+e^{-i2t})^2 ?
The solution to (e^{i2t}+e^{-i2t})^2 is 4cos^2(2t)