Question

If z = 3cis30°, z3 in rectangular form is _ + _i.

Please solve for the blanks.

Answer 1

Given that

z = 3 cis(30°)

z = 3 (cos(30°) + i sin(30°))

by DeMoivre's theorem it follows that

z³ = 3³ (cos(3×30°) + i sin(3×30°))

z³ = 27 (cos(90°) + i sin(90°))

z³ = 27 (0 + i)

z³ = 0 + 27 i