Posted by **Justin** on Sunday, May 23, 2010 at 11:18pm.

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.

- calculus -
**drwls**, Monday, May 24, 2010 at 7:12am
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"

- calculus -
**Justin**, Monday, May 24, 2010 at 8:49pm
Sorry for the misunderstanding. The X is a multiplication sign and the 4 is multiplied to the cubed root of 3.

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