# Find a product - give answer in polar form

• Mar 2nd 2009, 06:28 PM
kingscuba
Find a product - give answer in polar form
given

Z1= 2-2i Z2= (square root of 3)-i

i need help finding the answers for

Z1*Z2 and Z1/Z2

needs to find polar complex
• Mar 3rd 2009, 05:14 AM
lanzailan
z1=2-2j
=2.828/_-45 <<----polar form

z2=(3)^-1/2-j
=2/_-30 <<----- polar form

z1*z2=(2.828*2)/_-45+(-30)
=5.656/_-75

z1/z2=2.828/2*/_-45-(-30)
=1.414/_-15
• Mar 3rd 2009, 06:33 AM
HallsofIvy
The polar form that lanzailan gives is r and the angle (in degrees). For problems like this it is better to give the angle in radians: These complex numbers can be written as $\displaystyle 2\sqrt{2}(cos(\frac{\pi}{4})- sin(\frac{\pi}{4})$, $\displaystyle 2(cos(\frac{\pi}{6})+ sin(\frac{\pi}{6})$, or, equivalently, $\displaystyle 2\sqrt{2}e^{i\frac{\pi}{4}}$ and $\displaystyle 2e^{i\frac{\pi}{6}}$.

To find the product of two complex numbers, in complex form, you multiply the moduli (r values) and add the angles. To divide, divide the moduli and subtract the angles.