What is (cos(θ)+isin(θ))^2 ?

The solution to (cos(θ)+isin(θ))^2 is cos(2θ)+sin(2θ)i

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simplify (cos(θ)+isin(θ))^2

simplify

(cos (θ) + i sin (θ))^{2}

cos (2 θ) + sin (2 θ) i

Solution steps

(cos (θ) + i sin (θ))^{2}

Apply Perfect Square Formula:

(a + b)^{2} = a^{2} + 2 ab + b^{2}

(cos (θ) + i sin (θ))^{2} = cos^{2} (θ) + 2 cos (θ) i sin (θ) + (i sin (θ))^{2}

= cos^{2} (θ) + 2 cos (θ) i sin (θ) + (i sin (θ))^{2}

Simplify

cos^{2} (θ) + 2 cos (θ) i sin (θ) + (i sin (θ))^{2} : i sin (2 θ) + cos (2 θ)

= i sin (2 θ) + cos (2 θ)

Rewrite in standard complex form:

cos (2 θ) + sin (2 θ) i

= cos (2 θ) + sin (2 θ) i

(\frac{1}{2} x - \frac{2}{3} y) (\frac{1}{2} x + \frac{2}{3} y)

(x - 52)^{2}

(1 - \frac{x}{2})^{8}

\frac{x + 1}{( x ^{2} + 1 ) ^{2} ( x ^{2} + x + 1 )}

(x^{2} - 5) (x^{2} + 5)

What is (cos(θ)+isin(θ))^2 ?
The solution to (cos(θ)+isin(θ))^2 is cos(2θ)+sin(2θ)i