Complex number to exponential form

Question

How do you put the complex number  -2+i  into a form of  e^{ix} ?

       with i = sqrt(-1)

              x= angle between complex number and the real axis

Answer 1

z = -2 + i

 

z = re^iφ

 

r = √[(-2)² + (1)²] = √5

 

φ = tan^-1[1/(-2)]

 

Be sure to use radians, and be careful with the choice of quadrant.  In this problem, the quadrant of the phase angle φ is quadrant II (π > φ > π/2).

 

φ ≅ 2.6779 radians

 

z = √5 e^i2.6779

 

Test the answer:

 

Is -2 = √5 cos(2.6779) ?

Is 1 = √5 sin(2.6779) ?