What is (cos(t)+isin(t))^2(-sin(t)+icos(t)) ?

The solution to (cos(t)+isin(t))^2(-sin(t)+icos(t)) is -sin(2t+t)+cos(2t+t)i

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simplify (cos(t)+isin(t))^2(-sin(t)+icos(t))

simplify

(cos (t) + i sin (t))^{2} (- sin (t) + i cos (t))

- sin (2 t + t) + cos (2 t + t) i

Solution steps

(cos (t) + i sin (t))^{2} (- sin (t) + i cos (t))

Expand

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

= (i sin (2 t) + cos (2 t)) (- sin (t) + i cos (t))

Apply FOIL method

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

= i cos (2 t) cos (t) - i sin (2 t) sin (t) - sin (2 t + t)

Rewrite in standard complex form:

- sin (2 t + t) + (cos (2 t) cos (t) - sin (2 t) sin (t)) i

= - sin (2 t + t) + (cos (2 t) cos (t) - sin (2 t) sin (t)) i

Simplify

cos (2 t) cos (t) - sin (2 t) sin (t) : cos (2 t + t)

= - sin (2 t + t) + cos (2 t + t) i

\frac{1}{3} (- t^{3} + 2 - cot (t^{3} - 2))

sin (t) - y e^{t} (- t e^{- t} - e^{- t} + 1)

(x + 5 + x)^{2}

65 (\frac{8 π ^{3}}{3} + \frac{π}{2})

(x^{2} + 4)^{2} (x + 2 i)^{2}

What is (cos(t)+isin(t))^2(-sin(t)+icos(t)) ?
The solution to (cos(t)+isin(t))^2(-sin(t)+icos(t)) is -sin(2t+t)+cos(2t+t)i