Help in justifying complex number question

Given Z_{1 }and Z_{2} are two distinct complex numbers.

If |Z_{1}| = |Z_{2}|, then Re = 0

Is the above statement true or false?

Show working to justify your answer.

i managed to worked it out by letting z1= a+jb and z2= x+jy and then sub it in to work out and got true, not sure if i'm correct. Help is much appreciated (Nod)

Re: Help in justifying complex number question

Quote:

Originally Posted by

**tempq1** Given

and

are two distinct complex numbers.

If

, then Re

= 0

Is the above statement true or false?

Show working to justify your answer.

i managed to worked it out by letting z1= a+jb and z2= x+jy and then sub it in to work out and got true, not sure if i'm correct. Help is much appreciated

It is true. Messy to show.

Re: Help in justifying complex number question

Quote:

Originally Posted by

**tempq1** Given Z

_{1 }and Z

_{2} are two distinct complex numbers.

If |Z

_{1}| = |Z

_{2}|, then Re

= 0

Is the above statement true or false?

Show working to justify your answer.

i managed to worked it out by letting z1= a+jb and z2= x+jy and then sub it in to work out and got true, not sure if i'm correct. Help is much appreciated (Nod)

Representing z1 & z2 in exponential form we have:

Then:

Re: Help in justifying complex number question

Quote:

Originally Posted by

**MaxJasper** Representing z1 & z2 in exponential form we have:

Then:

You can note that:

and

I said it is messy.

Re: Help in justifying complex number question

Hello, tempq1!

. . . . .[1]

. .

. .

. .

. .

. . which, according to [1], equals 0.

Re: Help in justifying complex number question

Well I did say it is messy, but not that messy.

That is a notation nightmare.