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Polar Form of Complex Numbers

Conversion of a + bi to (a, b), (r, theta), and rcistheta.

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Polar Form of Complex Numbers

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Complete the table.
Word Definition
Reference angle ____________________________________________________________
rcisθ ____________________________________________________________

Polar Form

There are multiple forms a number can take. These five bullets all represent the same number:

  • complex number:   
  • rectangular point   
  • polar point: 

1) Plot the complex number 

a) What is needed in order to plot this point on the polar plane?
b) How could the r-value be determined?
c) What is the r for this point?
d) How could  be determined?
e) What is  for this point?
f) What would  look like on the polar plane?

2) What quadrant does  occur in when graphed?

3) What are the coordinates of z = -3 + 2i in polar form and trigonometric form?

4) What would be the polar coordinates of the point graphed below?


Change to polar form

Change to rectangular form
  1. For the complex number in standard form  find: a) Polar Form b) Trigonometric Form (Hint: Recall that and  )
Click here for answers.

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