Free Printable Complex Numbers for IB AA (HL)

1.

Which statement is false?

a)

b)

c)

d)

2.

Find $\left|z\right|$ for $z=2-2\sqrt{3}i$ .

a)

$2$

b)

$2\sqrt{3}$

c)

$\sqrt{3}$

d)

$4$

3.

Find $\arg\left(z\right)$ for $z=2-2\sqrt{3}i$ .

a)

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

b)

$-\frac{\pi}{6}$

c)

$\frac{\pi}{6}$

d)

$\frac{\pi}{3}$

4.

$w=\frac{z+1}{z-1},\ z=a+bi.\ Re\left(w\right)=?$

a)

$\frac{a^2+2a+1-b^2}{a^2+2a+1+b^2}$

b)

$\frac{2ab+2b}{a^2+2a+1+b^2}$

c)

$\frac{a^2+b^2-1}{a^2+b^2-2a+1}$

d)

$\frac{-2b}{a^2+b^2-2a+1}$

5.

a)

2

b)

4

c)

8

d)

16

e)

32

6.

Write the complex number in rectangular form.
3(cos210⁰ + isin210⁰)

a)

((-3√3)/2) - 3/2 i

b)

((3√3)/2) + 3/2 i

c)

-3i

d)

-3/2 +√3i

7.

Write the complex number in rectangular form.
4(cos7π/4 + isin7π/4)

a)

2√2 - 2√2i

b)

2√2 + 2√2i

c)

√2 + i

d)

2i- √2

8.

Find zw. Leave your answer in polar form.
z=2(cos40 + isin40)
w=4(cos20 + isin20)

a)

8(cos60 + isin60)

b)

-8(cos20 - isin20)

c)

6(sin60 + icos60)

d)

-4(cos20 +isin20)

9.

Find z/w. Leave your answer in polar form.
z=2(cos40 + isin40)
w=4(cos20 + isin20)

a)

1/2 (cos20 + isin20)

b)

1/4 (cos20 + isin20)

c)

8(cos60 - isin60)

d)

2(sin20 + isin60)

10.

Write the expression in the standard form a + bi.
[4(cos40 +isin40)]³

a)

-32 + 32√3i

b)

32 - 32√3i

c)

16√i +16

d)

4 + 4√i

11.

Write the expression in the standard form a + bi.
[3(cos80 +isin80)]³

a)

-27/2 - (27√3)/2 i

b)

27/2 + (27√3)/2 i

c)

9/2 + 3i

d)

27i + √3

12.

In the complex plane, the x-axis if referred to as the ____ axis and the y-axis is called the _____ axis

a)

real, imaginary

b)

imaginary, real

c)

complex, standard

d)

standard, cartesian

13.

Write in rectangular form

a)

A

b)

B

c)

C

d)

D

Complex Numbers for IB AA (HL)

Total questions: 13

Worksheet time: 29mins

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