# Need Help With Complex Numbers

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1. Feb 17, 2016

### Banker

1. The problem statement, all variables and given/known data
Question 3.b. - http://imgur.com/ztLiRvx

2. Relevant equations
For the sake of simplicity, lets assume that lambda = x.

3. The attempt at a solution
I tried equating the real an imaginary parts of arctan(1/4).
Real: x/2 + 3 = 4. This gives x = 2.
Imaginary: x/2 - 3 = 1. This gives x = 8.
I'm getting two different values of x(lambda).

2. Feb 17, 2016

### SammyS

Staff Emeritus
$\displaystyle arg(z) = tan^{-1}\left(\frac{Im(z)}{Re(z)}\right) \$

so you only know the ratio of the real to imaginary parts. It's not that the real part is 4 and the imaginary part is 1 .

3. Feb 17, 2016

### Staff: Mentor

???
I don't know what you're doing. arctan(1/4) means the angle (number) whose tangent is 1/4.
No.
If z = x I iy, then arg(z) = arctan(y/x).

Use the result from part a of this problem and the above to find $\lambda$ -- there is a single value.

4. Feb 18, 2016

### Banker

@Mark44 In my original attempt, I tried to reverse the process you mentioned, but as Sammy pointed out, it only tells the ratio.
So I then divided the equations for the imaginary and real parts in part 'a' and got 10 as my answer. So that will give 68 as the answer to the second part of 3.b, right?

5. Feb 18, 2016

### SammyS

Staff Emeritus
Yes, those are correct, although we generally like to see details of how you worked it out. That makes it easier for us to check your answer.

By the way, if you click on the big " Σ " in the blue menu bar at top of the message window, you will have easy access to many characters, including λ . Otherwise, it would be wise to use almost any other letter to represent λ, other than x, y, or z . Upper case L would have been a good choice.

Last edited: Feb 20, 2016
6. Feb 20, 2016

### Banker

7. Feb 20, 2016

### SammyS

Staff Emeritus