Question

Write the complex number -4 x 3^1/3 - 4i in exponential form.

I'm not sure how I use euler's formula to solve for this. A brief explanation would be greatly appreciated.

Answer 1

Does the "x" indicate multiplication, or is it an unknown? Does the 4 multi-ply (3^1/3) - 4i or just 3^(1/3) ?

Find the magnitude of the complex number first. Call it C. Then write your number as
C*e^(i*z)
using Euler's formula.
e^iz = cos z + i sin z

The magnitude of
-4 *(3^1/3 - 4i)
is
4*sqrt[3^(2/3) + 16] = 17.01
so you can write
-4 *(3^1/3 - 4i)
= 17.01*(-0.3392 +0.9406 i)
Now find the number z (in radians) for which
cos z = -0.3392 and sinz = 0.9406

It will be in the second quadrant
z = 1.9169

The answer would be 17.01 exp(1.9169i),

but it depends upon whether I interpreted what you wrote correctly. You need to use parenthese and explain the "x"

Answer 2

Sorry for the misunderstanding. The X is a multiplication sign and the 4 is multiplied to the cubed root of 3.