Concepts in complex numbers

What is the argument of the complex number (-2 - 2i)?

• 180 degrees or π radians

• 45 degrees or π/4 radians

• 90 degrees or π/2 radians

• -135 degrees or 3π/4 radians

Answer explanation

2020 HSC Q9

(5 was not an option)

in that year...

State: 56% correct

HAHS: 63% correct

Modulus of complex number  $\frac{1}{2}\ -\frac{\sqrt{3}}{2}\ i\ =$  

•  $1$  

•  $-2$  

•  $2$  

•  $\sqrt{2}$  

Find the modulus of the complex number. 

 $z=-4-7i$  

•  $\left|z\right|=\sqrt{56}$  

•  $\left|z\right|=65$  

•  $\left|z\right|=\sqrt{65}$  

•  $\left|z\right|=56$  

In the polar equation z = 6 (cos(45^o) + i sin(45^o), the argument is:

 $If\ Z=\frac{3+\sqrt{-1}}{2-\sqrt{-1}},\ modulus\ and\ conjugate\ of\ Z\ are$  

•  $1+i\ and\ \sqrt{2}$  

•  $2i\ and\ \sqrt{2}$  

•  $1-i\ and\ \sqrt{2}$  

•  $2\ and\ 2$  

What is the argument of z=3-6i?

• θ=2

• θ=9.36

• θ=2.33

• θ=-1.107

In the polar equation z = 6 (cos(45^o) + i sin(45^o), the modulus is:

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

•  $\frac{2\pi}{3}$  

•  $\frac{\pi}{3}$  

•  $-\frac{2\pi}{3}$  

•  $-\frac{\pi}{3}$  

What is the modulus of z=-5+2i

• 7i or 33