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Question
Write the complex number z = `(1 - i)/(cos pi/3 + i sin pi/3)` in polar form.
Solution
z = `(1 - i)/(cos pi/3 + i sin pi/3)`
= `(sqrt2[1/sqrt2 - i1/sqrt2])/(cos pi/3 + isin pi/3) =(sqrt2[cos(-pi/4) + isin(-pi/4)])/(cos pi/3 + isin pi/3)`
= `sqrt2[cos(-pi/4 - pi/3) + isin(-pi/4 - pi/3)]`
= `sqrt2[cos(-(7pi)/12) + isin(-(7pi)/12)]`
= `-sqrt2[cos (5pi)/12 + isin (5pi)/12]`
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