Free Printable complex number

1.

\left(-1\right)^{\frac{1}{3}}=?\ \ Choose\ correct\ options.

a)

-1

b)

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

c)

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

d)

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

e)

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

2.

$\frac{\left(3+i\right)^2}{1+i}$

a)

7+i

b)

7-i

c)

-7-i

d)

-7+i

3.

Find polar representation of (-1-i)

a)

$\sqrt{2}\left(\cos\ \frac{\pi}{4}-i\ \sin\ \frac{\pi}{4}\right)$

b)

$\sqrt{2}\left(\cos\ \frac{\pi}{4}+i\ \sin\ \frac{\pi}{4}\right)$

c)

$\sqrt{2}\left(\cos\ \frac{3\pi}{4}+i\ \sin\ \frac{3\pi}{4}\right)$

d)

$\sqrt{2}\left(\cos\ \frac{3\pi}{4}-i\ \sin\ \frac{3\pi}{4}\right)$

4.

which of the following statement is correct.

a)

i = 2i

b)

i < 2i

c)

i > 2i

d)

can not be compared.

5.

$Find\ \ \left(1+w-w^2\right)^3\ +\left(1+w^2-w\right)^3$

a)

16

b)

-16

c)

0

d)

non of these

6.

$Find\ \left(2+3w+3w^2\right)^7$

a)

1

b)

0

c)

2

d)

-1

7.

$find\ \frac{1}{i^{17}}$

a)

1

b)

i

c)

-i

d)

-1

8.

$choose\ the\ correct\ options\ \ \sqrt{i}\ =\ ?$

a)

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

b)

$-\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{2}}i$

c)

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

d)

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

9.

$\overline{z}+z\ =?$

a)

2z

b)

2 Re(z)

c)

2i Im(z)

d)

Non of the above

10.

Find the real and imaginary part for reciprocal of 2-3i.

a)

$\frac{2}{13},\ -\frac{3}{13}$

b)

$\frac{2}{13},\ -\frac{3}{13}i$

c)

$\frac{2}{13},\ \frac{3}{13}i$

d)

$\frac{2}{13},\ \frac{3}{13}$

11.

$z\ =\overline{z}\ \ \ \ \ \Longleftrightarrow\ \ \ _{...................................}$

a)

z=0

b)

z is a real number

c)

z is a purely imaginary number.

d)

Non of the above.

12.

$If\ \ z^2=\ -1\ then$

a)

$z=\pm1$

b)

$z=\pm i$

c)

$z=\pm\left(1+i\right)$

d)

Non of the above

13.

a)

True

b)

false

14.

Which of the following is the reciprocal of i.

a)

-i

b)

i

c)

1

d)

-1

15.

Conjugate of 2i is

a)

2i

b)

1/2i

c)

-2i

d)

-2

16.

What is the value of r if z= 3 + 5 i

a)

6

b)

34

c)

36

d)

$\sqrt{34}$

17.

$Find\ the\ principal\ value\ of\ \arg ument\ for\ \ \frac{1}{2}-\frac{\sqrt{3}}{2}i$

a)

$\frac{2\pi}{3}$

b)

$\frac{\pi}{3}$

c)

$-\frac{2\pi}{3}$

d)

$-\frac{\pi}{3}$

18.

$\left(-i\right)^{\left(4n-1\right)}=?$

a)

-i

b)

i

c)

1

d)

-1

19.

$If\ z_1\ and\ z_2\ have\ \arg uments\ 35\degree\ and\ 36\degree,\ then\ the\ \arg ument\ of\ \left(z_1z_{2\ }\right)\ is$

a)

$35\degree$

b)

$71\degree$

c)

$36\degree$

d)

$1\degree$

20.

$Find\ \ w^{218}$

a)

0

b)

1

c)

w

d)

$w^2$

complex number

Total questions: 20

Worksheet time: 26mins

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