Complex Numbers Forms?

Question

Write in polar form:

a) πi

Write in the form a+bi:

b) e^(-πi/4)

c) e^(1+πi)

d) e^(3+i)

Answer 1

pi * i =>

pi * (0 + i) =>

pi * (cos(pi/2) + i * sin(pi/2)) =>

(e^ln(pi)) * e^((pi/2) * i) =>

e^(ln(pi) + (pi/2) * i)

e^((-pi/4) * i) =>

(cos(-pi/4) + i * sin(-pi/4)) =>

(sqrt(2)/2  -  (sqrt(2)/2) * i) =>

(sqrt(2)/2) * (1 - i)

e^(1 + pi * i) =>

e * (cos(pi) + i * sin(pi)) =>

-e

e^(3 + i) =>

(e^3) * (cos(1) + i * sin(1))