Representing complex numbers

For z =  $1\ +\ \sqrt{3}i$  , what is the modulus?

What is the modulus for a complex number?

• $r=\sqrt{a^2-b^2}$

• $r=\sqrt{a^2-\left(bi\right)^2}$

• $r=\sqrt{a^2+b^2}$

• $r=\sqrt{a^2+\left(bi\right)^2}$

Find the modulus of the complex number. 

 $z=3+i$  

•  $\left|z\right|=10$  

•  $\left|z\right|=\sqrt{10}$  

•  $\left|z\right|=2$  

•  $\left|z\right|=\sqrt{2}$  

• 13

• 5

• 5i

Consider the complex number in the graph. Given that the argument must be between -π < θ < π, what can you say about the argument, θ?

• θ is negative and -π < θ < -π/2

• θ is negative and -π/2 < θ < 0

• θ is positive and π/2 < θ < π

• θ is positive and 0 < θ < π/2

Answer explanation

What is the argument of the complex number -1 - √3i?

• 180 degrees

• 45 degrees

• -60 degrees

• 120 degrees

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

•  $1$  

•  $-2$  

•  $2$  

•  $\sqrt{2}$  

Find argument for p=3-i

Argument of complex number   $1\ -\ i\ =$  

•  $\frac{\pi}{4}$  

•  $\frac{-\pi}{4}$  

•  $\frac{3\pi}{4}$  

•  $\frac{-3\pi}{4}$