## Example 1.2.11 (c): Polar coordinates examples |

Convert the following numbers into the indicated coordinates and draw them in the complex plane: |

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 ]