What is (cos(x)+i*sin(x))^2 ?

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

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simplify (cos(x)+i*sin(x))^2

simplify

(cos (x) + i \cdot 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

A (- 4, 3) y B (2, - 5)

(3 x + \frac{\frac{4}{5}}{x})^{8}

\frac{225 ( e ^{2} - 1 )}{4}

x (300 - \frac{x}{20})

x^{3} e^{x} - 3 (x^{2} e^{x} - 2 (e^{x} x - e^{x}))

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