Rect & Polar Complex Numbers Quiz

In the complex plane, the ____________ is the distance from the origin to the complex number point z.

The _________________ is the radian or degree measure of the counter clockwise rotation of the vector representing complex number z.

The rectangular form of a complex number is written as z = a + bi, with (a, b) representing the point in the complex plane. Which of the following represent that point as written in polar form?

•  $\left(\sin\ \theta,\ \cos\ \theta\right)$  
  

•  $\left(\cos\ \theta,\ \sin\ \theta\right)$  

•  $\left(\tan\ \theta,\ \cos\ \theta\right)$  

•  $\left(\tan\ \theta,\ \sin\ \theta\right)$  

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

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

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

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

Convert to rectangular form:
z =  $2\left(\cos\left(45^o\right)+\ i\ \sin\left(45^o\right)\right)$  

• z = 2 + 2i

• z = 1 + 2i

•  $z\ =\frac{\sqrt{2}}{2}\ +\ \frac{\sqrt{2}}{2}\ i$ 

•  $z\ =\ \sqrt{2}+\sqrt{2}i$  

Convert to polar form:

z = -3 + 3i

• z = $3\sqrt{2}\left(\cos\left(135^o\right)+\sin\left(135^o\right)\right)$

• z = $3\sqrt{2}\left(\cos\left(45^o\right)+\ i\ \sin\left(45^o\right)\right)$

• z = $\sqrt{6}\left(\cos\left(135^o\right)+\ i\ \sin\left(135^o\right)\right)$

• z = $\sqrt{6}\left(\cos\left(45^o\right)+i\ \sin\left(45^o\right)\right)$