SOLUTION: Question: Consider the complex number -1 + sqrt(3)i a) Write this number in polar form b) Find all solutions of z^3= -1 + sqrt(3)i c) Find all values of log (-1 + sqrt(3)i) d)

Question 810442: Question: Consider the complex number -1 + sqrt(3)i
a) Write this number in polar form
b) Find all solutions of z^3= -1 + sqrt(3)i
c) Find all values of log (-1 + sqrt(3)i)
d) Find all values of (-1 + sqrt(3)i)^2+i
I have immense trouble with this stuff, just started the course after a decade of no math of any kind, just re-learning the basics. I tried a, got this far:
a) z=a + bi; -1 + sqrt(3)i in polar form: r= sqrt [(-1)^2 + sqrt(3)^2]
r= sqrt (4) = 2
theta = tan (b/a) = tan[sqrt(3)/-1)]
theta = -1.047 = -0.333 pi
*I get lost figuring out which quadrant the complex number is in after this
*I gave up on all of the other questions after this
*How is my notation in this message ? Can you read my questions easily enough, or are there better ways to present the data.
Thank you for any/all help
Answer by oscargut(2103) (Show Source): You can put this solution on YOUR website!
this question is so long
I do part a) here:
a) Answer: radius = 2 , angle = 120 degrees
You can ask me more at : mthman@gmail.com
Thanks

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