What is (cos(x)+isin(x))^2 ?

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

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simplify (cos(x)+isin(x))^2

simplify

(cos (x) + i sin (x))^{2}

cos (2 x) + sin (2 x) i

Solution steps

(cos (x) + i sin (x))^{2}

Apply Perfect Square Formula:

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

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

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

Simplify

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

= i sin (2 x) + cos (2 x)

Rewrite in standard complex form:

cos (2 x) + sin (2 x) i

= cos (2 x) + sin (2 x) i

(cos (x) + i sin (x))^{5}

(x + y i)^{4}

(3 + i)^{7}

(x + 2)^{2}

(tan (x) + 1)^{2}

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