Example 1.2.11 (c): Polar coordinates examples

Convert the following numbers into the indicated coordinates and draw them in the complex plane:
  • Prove that if z = r cis(t) then = r cis(-t)
Context Context

If z = r cis(t) then we have in rectangular coordinates that z = x+iy with

x = r cos(t)
y = r sin(t)

But the vector r cis(-t) has coordinates

r cos(-t) = r cos(t) = x
r sin(-t) = -r sin(t) = -y

because cos is even and sin is odd. Thus r cis(-t) = x - i y = .

[ x ]

Interactive Complex Analysis, ver. 1.0.0
(c) 2006-2007, Bert G. Wachsmuth
Page last modified: May 29, 2007