# Need Help With Complex Numbers

## Homework Statement

Question 3.b. - http://imgur.com/ztLiRvx

## Homework Equations

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

## 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).

SammyS
Staff Emeritus
Homework Helper
Gold Member

## Homework Statement

Question 3.b. - http://imgur.com/ztLiRvx

## Homework Equations

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

## 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).
##\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 .

Banker
Mark44
Mentor

## Homework Statement

Question 3.b. - http://imgur.com/ztLiRvx

## Homework Equations

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

## The Attempt at a Solution

I tried equating the real an imaginary parts of arctan(1/4).
???
I don't know what you're doing. arctan(1/4) means the angle (number) whose tangent is 1/4.
Banker said:
Real: x/2 + 3 = 4. This gives x = 2.
Imaginary: x/2 - 3 = 1. This gives x = 8.
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.
Banker said:
I'm getting two different values of x(lambda).

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?

SammyS
Staff Emeritus
Homework Helper
Gold Member
@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?
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:
SammyS
Staff Emeritus