What is the value of (cos(pi/4)+isin(pi/4))^{100} ?

The value of (cos(pi/4)+isin(pi/4))^{100} is -1

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(cos(pi/4)+isin(pi/4))^{100}

(cos (\frac{π}{4}) + i sin (\frac{π}{4}))^{100}

- 1

Solution steps

(cos (\frac{π}{4}) + i sin (\frac{π}{4}))^{100}

Refine to a decimal form

= - 1

sin (6 \frac{π}{9})

cos (\frac{π}{5}) cos (\frac{2 π}{15}) - sin (\frac{π}{5}) sin (\frac{2 π}{15})

3 cos (5.3 π)

(2 (cos (\frac{π}{4}) + i sin (\frac{π}{4})))^{6}

cos (\frac{π}{2} - \frac{π}{6})

What is the value of (cos(pi/4)+isin(pi/4))^{100} ?
The value of (cos(pi/4)+isin(pi/4))^{100} is -1