Question

Write the complex number z = `(1 - i)/(cos  pi/3 + i sin  pi/3)` in polar form.

Answer 1

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]`