What is the real component of the complex number 5 x e ^ (0.57i)?

Question

What is the value of A in the equation:
-9+-9i = A x e ^ (i \phi)

What is the value of phi in the equation:
4.5 + 3.6i = A x e ^ (i \phi)
answer in degrees or specify the unit "rad" to give it in radians

regards,

Answer 1

1. 5 x e ^ (0.57i) = 4.20950488 + 2.69816024 i
you can now see here the real part of the complex number...
§

2. A is essentially the distance from the origin (the magnitude)
Thus A = 9sqrt2.

3. phi is the angle thus tan[phi] = y/x...
tan[phi] = 3.6/4.5 = 0.8
phi = arctan 0.8 = 38.66 degrees

Answer 2

Part 1
5 e^(0.571) = 5 (cos 0.571 + i sin 0.571)
Real component , R = 5 cos 0.571
R = 0.842

Part 2
A² = (- 9) ² + 9 ²
A ² = 81 + 81
A ² = 162
A = 9√2

Part 3
Reading this as:-
4.5 + 3.6 i = A e^(i Ø)
Ø = tan^(-1) (3.6 / 4.5)
Ø = 38.7 °