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Complex Numbers: Multiplying and Dividing in Polar form

If

z =

6 ( –  1 2 √2 –  1 2 √2 j )

then the complex number 4 z³ in polar form is r ( cos θ + j sin θ ) where

r = and θ = degreesradians to 3 dps.

Worked Solution:

4 has modulus 4 and argument 0°
z has modulus 6 and argument –135°

Power of a complex polar number: |u^p| = |u|^p and arg(u^p) = p arg(u)

   z³ has modulus 6³ = 216 and argument 3× –135 = –405° = –45°

Multiplication of complex polar numbers: |u×v| = |u|×|v| and arg(u×v) = arg(u) + arg(v)

4

z3

has modulus

4×216

= 864

and argument

0° + –45° =

–45° = –0.785 radians

© MEI Produced by Dr Ron Knott, 10 April 2007

Test reference: ComplexPolarMulDiv.html?ref=52685