How to write (6-6i)/(-sqrt(3)+i) in exponential form re^((i)(θ))?

Question

I am getting 4.242640687 for r which is correct.
For theta, i am getting -3.403392041 which the system for my online homework is telling me im wrong. not sure where i went wrong tho.

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Answer 1 · 2018-06-22T05:53:51

Please seee the explanation below.

The numerator is

#z=6-6i#

#z=6(1-i)#

#=6sqrt2(1/sqrt2-i/sqrt2)#

#=6sqrt2(cos(-pi/4)+isin(-pi/4))#

#=6sqrt2e^(-ipi/4)#

The denominator is

#z_1=-sqrt3+i#

#=2(-sqrt3/2+i/2)#

#=2(cos(5/6pi)+isin(5/6pi))#

#=2e^(i5/6pi)#

Theefore,

#z/z_1=(6sqrt2e^(-ipi/4))/(2e^(i5/6pi))#

#=3sqrt2e^(-i(1/4+5/6)pi)#

#=3sqrt2e^(-i13/12pi)#

#-13/12pi=11/12pi#

Therefore,

#r=3sqrt2# and #theta=11/12pi#

I got the same result for #r# and for #theta#, can you try #theta=11/12pi=2.88#