Converting 1+i to Polar Form

Complex Analysis · Axiom Academy

EXAMPLE Converting to Polar Form Turn the rectangular number 1 + i into polar form by finding its modulus and argument. Convert the complex number z = 1 + i into polar form , where r is the modulus and is the argument. Nicely done. You converted a rectangular number to polar form by finding how far it is from the origin and what angle it makes. Modulus: is the distance from the origin — here . Argument: , but always check the quadrant. In Quadrant I, works directly. Result: , which multiplies back out to exactly 1 + i . Modulus-and-argument is the same recipe for any a + bi — the quadrant of the point is the only thing that changes which angle the argument lands on.

This is the written version of the interactive lesson above. See the full Complex Analysis course.