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
using Euler's formula.
e^iz = cos z + i sin z
The magnitude of
-4 *(3^1/3 - 4i)
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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