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

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

Conversion from polar to rectangular is easy, using

x = r cos(t)

y = r sin(t)

**For z:** we have that length

x = r cos(t) = 2 cos(0) = 2

y = r sin(t) = 2 sin(0) = 0

**For w:** we have that length

x = r cos(t) = 3 cos() = -3

y = r sin(t) = 3 sin() = 0

**For v:** we have that length

x = r cos(t) = 2 cos(5/6) = -2*1/2* = -

y = r sin(t) = 2 sin(5/6) = 2*1/2 = 1

**For u:** we have that length

x = r cos(t) = 2 cos(-3/4) = 2*(-1/2)* = -

y = r sin(t) = 2 sin(-3/4) = 2*(-1/2)* = -

You should confirm these computations by drawing the various vectors.