# Magnitude of a complex number

1. Oct 21, 2008

### Benzoate

1. The problem statement, all variables and given/known data

calculate the magnitude of z= i/(6i-3) and the argument of the real and imaginary parts
2. Relevant equations

3. The attempt at a solution

z=i/6i-3

z*=i/-3+6i?

mag(z)=zz*

not sure if z* is correct.

Last edited by a moderator: Oct 21, 2008
2. Oct 21, 2008

### Staff: Mentor

In that kind of problem, you want to get the imaginary numbers out of the denominator. What can you multiply both the top and bottom by, to get rid of the complex denominator?

3. Oct 21, 2008

### Benzoate

zz*=i/6i-3*(-3+6i/-3+6i)=6-3i/(45)=
sqrt((6/45)^2+(3/45)^2)=.15=mag(z)

how would I fine arg(z),Re(z),and Im(z)?

4. Oct 22, 2008

### Staff: Mentor

Don't try to do ZZ* first. Show us how you rationalize the denominator first, okay?

5. Oct 22, 2008

### HallsofIvy

Staff Emeritus
The complex conjugate of i/(6i- 3) is -i/(-6i-3)= i/(6i+3). You need the negative on both "i"s.

But as Berkman said, it is better to get z in the form a+ bi first by rationalizing the denominator.