Free Printable de Moivre's Theorem

1.

The value of

\left(1+i\sqrt{3}\right)^6

is

a)

64

b)

-64

c)

1

d)

2

2.

The value of

\frac{1}{\left(\cos\theta+i\sin\theta\right)^6}

is

a)

$-\cos6\theta-i\sin6\theta$

b)

$\cos6\theta+i\sin6\theta$

c)

$\cos6\theta-i\sin6\theta$

d)

$-\cos6\theta+i\sin6\theta$

3.

$\left(\cos\ \frac{\pi}{6}\ -\ i\sin\ \frac{\pi}{6}\right)^{12}\ is\ equal\ to$

a)

-i

b)

-1

c)

i

d)

1

4.

$\cos4\theta$ is eqauivalent to

a)

$8\cos^4\theta+8\cos^2\theta+1$

b)

$8\cos^4\theta-8\cos^2\theta+1$

c)

$8\cos^4\theta-8\cos^2\theta-1$

d)

$8\cos^4\theta+8\cos^2\theta-1$

5.

$\sin4\theta$ is equivalent to

a)

$8\cos^3\theta\sin\theta+8\cos\theta\sin^3\theta$

b)

$4\cos^3\theta\sin\theta+4\cos\theta\sin^3\theta$

c)

$4\cos^3\theta\sin\theta-4\cos\theta\sin^3\theta$

d)

$8\cos^3\theta\sin\theta-4\cos\theta\sin^3\theta$

6.

$If\ z\ =\ \cos\theta\ +i\sin\theta,\ the\ value\ of\ z^3+\frac{1}{z^3}\ is$

a)

$2\cos3\theta$

b)

$\cos3\theta$

c)

$i\sin3\theta$

d)

$2i\sin3\theta$

7.

$-4\sqrt{3}+4i$ can be expressed in the form $re^{i\theta}$ as

a)

$8e^{\frac{5\pi i}{6}}$

b)

$8e^{-\frac{\pi i}{6}}$

c)

$4e^{\frac{5\pi i}{6}}$

d)

$4e^{-\frac{\pi i}{6}}$

8.

Which of the following is correct?

a)

$e^{2\theta i}=\sin2\theta+i\cos2\theta$

b)

$e^{2\theta i}=\cos\theta+2i\sin\theta$

c)

$e^{2\theta i}=\cos2\theta+i\sin2\theta$

d)

$e^{2\theta i}=2\left(\cos\theta+i\sin\theta\right)$

9.

$e^{-i\pi}$ is equal to

a)

-i

b)

i

c)

1

d)

-1

10.

$e^{1+i\theta}$ is equal to

a)

$e^{\cos\theta+i\sin\theta}$

b)

$e\left(\cos\theta+i\sin\theta\right)$

c)

$\cos\left(1+i\right)+j\sin\left(1+i\right)$

d)

$ei\sin\theta$

de Moivre's Theorem

Total questions: 10

Worksheet time: 9mins

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