# Thread: Complex Analysis

1. ## Complex Analysis

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

2. Originally Posted by HenrySellers
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.

3. I actually havent seen any examples, I genuinely dont understand. Maybe if someone guided me through the first one I could learn that way. And im not doin any course, im just learning myself!

4. 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.

5. Using the above definitions, we have:
1. log(2 − 2i) and observe that |2 - 2i| = 2√2, and the argument is 7pi/4
Can you plug these into the formula for log(z)?

p.s. Don't call me Shirley.

6. did you get anywhere on this im stuck on the exact same questions!!