Powers and roots of complex numbers

2010004610

Level:

Identify the complex number that equals to

(\sqrt{3} - i)^{37}

2^{36} (\sqrt{3} - i)

2^{36} (- 1 + i \sqrt{3})

2^{36} (\sqrt{3} + i)

2^{36} (- 1 - i \sqrt{3})

2010004609

Level:

Evaluate

(2 + 2 i)^{100}

and write the result in algebraic form.

- 2^{150}

- 2^{150} i

2^{150} i

2^{150}

2010004608

Level:

Evaluate

(1 + i)^{22}

and write the result in algebraic form.

- 2^{11} i

2^{11} i

2^{22} i

- 2^{22} i

2010004607

Level:

Evaluate

(\cos 27^{\circ} + i \sin 27^{\circ})^{5}

and find the algebraic form of the result.

- \frac{\sqrt{2}}{2} + \frac{\sqrt{2}}{2} i

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

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

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

2010004606

Level:

Evaluate

(\cos 33^{\circ} + i \sin 33^{\circ})^{10}

and find the algebraic form of the result.

\frac{\sqrt{3}}{2} - \frac{1}{2} i

\frac{\sqrt{3}}{2} + \frac{1}{2} i

\frac{1}{2} + \frac{\sqrt{3}}{2} i

\frac{1}{2} - \frac{\sqrt{3}}{2} i

2010004605

Level:

Find the algebraic form of the complex number:

{(\frac{1}{2} + \sin \frac{π}{6} + i \sin \frac{π}{2})}^{3}

- 2 + 2 i

2 - 2 i

- 2 - 2 i

2 + 2 i

2010004604

Level:

Find the algebraic form of the complex number:

{(\cos \frac{π}{3} + i \sin \frac{π}{3})}^{5}

\frac{1}{2} - i \frac{\sqrt{3}}{2}

\frac{\sqrt{3}}{2} + i \frac{1}{2}

\frac{\sqrt{3}}{2} - i \frac{1}{2}

\frac{1}{2} + i \frac{\sqrt{3}}{2}

2010004603

Level:

Identify a complex number that is not equal to

{(\cos \frac{π}{6} + i \sin \frac{π}{6})}^{13}

\frac{\sqrt{3}}{2} - \frac{1}{2} i

\frac{\sqrt{3}}{2} + \frac{1}{2} i

\cos \frac{π}{6} + i \sin \frac{π}{6}

\cos \frac{25 π}{6} + i \sin \frac{25 π}{6}

2010004602

Level:

Identify a complex number that is not equal to

{(\cos \frac{π}{3} + i \sin \frac{π}{3})}^{19}

\frac{1}{2} - \frac{\sqrt{3}}{2} i

\cos \frac{π}{3} + i \sin \frac{π}{3}

\frac{1}{2} + \frac{\sqrt{3}}{2} i

\cos (- \frac{5 π}{3}) + i \sin (- \frac{5 π}{3})

2010004601

Level:

Evaluate

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

and find the algebraic form of the result.

1

- 1

- i

i

Powers and roots of complex numbers

2010004610

2010004609

2010004608

2010004607

2010004606

2010004605

2010004604

2010004603

2010004602

2010004601

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