# How do you divide the following in polar form? (2-2i)/(-1-i)Please express the answer in Pi Multiple form and show each part of the problem in polar form

Asked on by s412889

justaguide | College Teacher | (Level 2) Distinguished Educator

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To divide the given complex numbers using the complex form of complex numbers we have to first convert each of the complex numbers into the complex form. Any complex number of the form z = x + i*y can be written as |z|<A>, where the absolute value |z| = sqrt ( x^2 + y^2) and the argument A = arc tan ( y/x)

2 - 2i = (sqrt(2^2 + 2^2)) <arc tan (-2/2)>

=> 2*sqrt 2 <- pi/4>

-1 - i =  (sqrt(1^2 + 1^2)) <arc tan (-1/ - 1)>

=> sqrt 2 <-3*pi/4>

The result when the two complex numbers are divided is given by dividing the absolute value and finding the difference of the arguments.

=> (2*sqrt 2/ sqrt 2) <-pi/4 + 3*pi/4>

=> 2 < pi/2 >

The result of dividing the complex numbers is 2 <pi/2>

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