Question and my solution below.
Which part did I do wrong?

Question

Question and my solution below.
Which part did I do wrong?

owlet · Answer

attachment

owlet · Answer

This is a review question  and my book only has the solution & answers to odd number questions and this is an even number question. My answer is not even one of the choices lol

hartnn · Answer

I see no error in your working...

owlet · Answer

are you sure? maybe the book is wrong. thanks for confirming it :)
I'll probably ask  my prof about that.

hartnn · Answer

yup http://www.wolframalpha.com/input/?i=cube+roots+of+%28-3-3i%29

irishboy123 · Answer

you are starting with $$\sqrt[3] { -3e^{\frac {\pi } {4}  } }  $$??

owlet · Answer

why is it  -3? 
r is equal to $\sqrt{18}$, so I have multiply it by the nth power which is 1/3 
so it will be $\sqrt[6]{18}$ since 1/2 times 1/3 is 1/6.

De moivres + euler's formula: $\large z^n=r^ne^{in \theta}$
sub the values in..it will be: $\large z^{1/3}=\sqrt[6]{18}e^{i \frac{1}{3}( \frac{5 \pi}{4} + 2 \pi k)}$

irishboy123 · Answer

if we draw it first we have this

|dw:1442695851885:dw|

which kinda makes it easy as we have $3 e^{i \frac{5 \pi}{4}}$