How Do You Calculate the Magnitude and Argument of a Complex Number?

[Benzoate]

Homework Statement

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

Homework Equations

The Attempt at a Solution

z=i/6i-3

z*=i/-3+6i?

mag(z)=zz*

not sure if z* is correct.

 

[berkeman]

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?

 

[Benzoate]

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 co8mplex denominator?

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)?

 

[berkeman]

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)?

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

 

[HallsofIvy]

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.