Hi guys, not sure where to start on this, i know i = root -1 but thats about it!
Find all values of :
1. log(2 − 2i)
2. (1 − i)^2+i
3. tan−1(2i)
4. (2i + 2)^1/4
When you write "not sure where to start on this" what do you mean?
Surely you are in some sort of course studying complex numbers.
And surely that course has text material.
You should also understand that this is not a homework service nor is it a tutorial service. Please either post some of your own work on this problem or explain what you do not understand about the question.
Then why are you trying to do something you have never seen?
In order to do any of these you need two basic concepts.
What is the value of the absolute value of a complex number, $\displaystyle |z|$.
You need to find the argument of a complex number, $\displaystyle \arg(z)$.
We define $\displaystyle \log(z)$ as $\displaystyle \ln(|z|)+i(\arg(z)+2k\pi)$
We define $\displaystyle z^w$ as $\displaystyle \exp(w\log(z)) $.
It usually takes three to six weeks in basic complex variables to reach this point in the material. We will not do the course here.