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Popular >

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

Solution

simplify

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

Solution

- 4 sin^{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}

Expand

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

= (2 i sin (z))^{2}

Apply exponent rule:

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

= 2^{2} i^{2} sin^{2} (z)

2^{2} = 4

= 4 i^{2} sin^{2} (z)

i^{2} = - 1

= 4 (- 1) sin^{2} (z)

Refine

= - 4 sin^{2} (z)

Popular Examples

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

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

expand (1-sin(2x))^2 expand

(1 - sin (2 x))^{2}

expand x^{2/3}(x-1)expand

x^{\frac{2}{3}} (x - 1)

expand (e^x-2)^2 expand

(e^{x} - 2)^{2}

simplify 1/2+1/4 (1.2-1)simplify

\frac{1}{2} + \frac{1}{4} (1.2 - 1)

Frequently Asked Questions (FAQ)

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