What is ((cos(θ)+isin(θ)))^3 ?

The solution to ((cos(θ)+isin(θ)))^3 is (4cos^3(θ)-3cos(θ))+(3sin(θ)-4sin^3(θ))i

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simplify ((cos(θ)+isin(θ)))^3

simplify

((cos (θ) + i sin (θ)))^{3}

(4 cos^{3} (θ) - 3 cos (θ)) + (3 sin (θ) - 4 sin^{3} (θ)) i

Solution steps

(cos (θ) + i sin (θ))^{3}

Expand

(cos (θ) + i sin (θ))^{3} : cos^{3} (θ) + 3 cos^{2} (θ) sin (θ) i - 3 sin^{2} (θ) cos (θ) - sin^{3} (θ) i

= cos^{3} (θ) + 3 cos^{2} (θ) sin (θ) i - 3 sin^{2} (θ) cos (θ) - sin^{3} (θ) i

Rewrite in standard complex form:

(4 cos^{3} (θ) - 3 cos (θ)) + (3 sin (θ) - 4 sin^{3} (θ)) i

= (4 cos^{3} (θ) - 3 cos (θ)) + (3 sin (θ) - 4 sin^{3} (θ)) i

c H (r (o, s, x), o, s, x) a d r (o, s, x) a d os (x - 2 x = 6)

\frac{12.9}{( s + 1.1 ) ( s + 2 )}

6 sin (x) (x + 1)

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

\frac{x}{( x + 2 ) ( x + 3 )}

What is ((cos(θ)+isin(θ)))^3 ?
The solution to ((cos(θ)+isin(θ)))^3 is (4cos^3(θ)-3cos(θ))+(3sin(θ)-4sin^3(θ))i