Powers and roots of complex numbers

9000070104

Level:

Evaluate the following complex number.

{(\sin 2 π + i \cos 2 π)}^{11}

- i

- 1

1

i

9000070105

Level:

Evaluate the following complex number.

i^{13}

\cos \frac{π}{2} + i \sin \frac{π}{2}

\cos \frac{π}{2} - i \sin \frac{π}{2}

\sin \frac{π}{2} + i \cos \frac{π}{2}

\cos \frac{3 π}{2} + i \sin \frac{3 π}{2}

9000037404

Level:

Given

z = \sqrt{2} (\cos \frac{π}{3} - i \sin \frac{π}{3})

, find

z^{2}

- 1 - i \sqrt{3}

1 + i \sqrt{3}

- 2 - i \sqrt{2}

2 + i \sqrt{2}

9000037403

Level:

Given

z = \sqrt{3} (\cos \frac{π}{3} + i \sin \frac{π}{3})

, find

z^{4}

- \frac{9}{2} - \frac{9 i \sqrt{3}}{2}

\frac{9}{2} + \frac{9 i \sqrt{3}}{2}

\frac{3}{2}

- \frac{3}{2}

9000037405

Level:

Evaluate

{(1 + i)}^{7}

8 - 8 i

7 - 7 i

1

- i

9000037406

Level:

Evaluate

{(\cos \frac{π}{4} + i \sin \frac{π}{4})}^{40}

1

1 + i

i

1 - i

9000037407

Level:

Evaluate

{(\cos \frac{π}{2} + i \sin \frac{π}{2})}^{13}

and find the algebraic form of the result.

i

1 + 2 i

1 - i

1

9000037410

Level:

Evaluate

{(1 - i)}^{3}

- 2 - 2 i

2 + 2 i

1 + i

i

9000035709

Level:

Simplify

(1 - i)^{- 3}

- \frac{1}{4} + \frac{1}{4} i

1 + 3 i

- 2 - 2 i

\frac{1}{2} + \frac{1}{2} i

9000035809

Level:

Given the complex number

z = - 1 + i

, find the angle in the polar form of the number

z^{6}

\frac{π}{2}

\frac{3 π}{2}

\frac{3 π}{4}

\frac{7 π}{4}

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Powers and roots of complex numbers

9000070104

9000070105

9000037404

9000037403

9000037405

9000037406

9000037407

9000037410

9000035709

9000035809

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