Find a product - give answer in polar form

**kingscuba** · March 2nd 2009, 06:28 PM

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

**lanzailan** · March 3rd 2009, 05:14 AM

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

**HallsofIvy** · March 3rd 2009, 06:33 AM

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 $2\sqrt{2}(cos(\frac{\pi}{4})- sin(\frac{\pi}{4})$ , $2(cos(\frac{\pi}{6})+ sin(\frac{\pi}{6})$ , or, equivalently, $2\sqrt{2}e^{i\frac{\pi}{4}}$ and $2e^{i\frac{\pi}{6}}$ .

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.

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