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Complex Numbers With Logarithms!

I'm not really sure how to go about solving these, by 'principal values' I assume the values you get from finding the argument right?

For Question 14 would I use laws of logs to solve?

Reply 1

Mark13

Original post by As_Dust_Dances_

I'm not really sure how to go about solving these, by 'principal values' I assume the values you get from finding the argument right?

For Question 14 would I use laws of logs to solve?

Basically, there are many values the logarithm of a complex number could take - you could say log(1)=0, because e^0=1, but equally e^(2pi i)=1, so you could say log(1)=2pi i.

To get around this, we say that the principal value of the logarithm of a complex number is the one whose imaginary part is greater than -pi, and less than or equal to pi.

Reply 2

As_Dust_Dances_

Original post by Mark13

Thanks for your help, took me a while to understand it but essentially you can write it in the form (which I think is what you were saying)

log(z) = ln|z| + i arg(z) which is how I solved it.

Thanks again! :smile: