# Thread: Complex Number in its simplest form

1. ## Complex Number in its simplest form

Hi all. Not sure whether this is correct or not and I would like some guidance! Thanks...

Given that z1 = 4-j5 and z2 = -3+j4, Find the compelx number z1/z1-z2 in its simplest form.

This is what I have...

z1 / (z1 -z2) = (4 - j5) / (4 - j5 +3 -j4) = (4-j5)/(7 - j9)

=[ (4-j5) x (7+j9) ] / [ (7-j9) x (7+j9) ]

=[ (4x7 - (-5) 9) + j(4x9+(-5)x7) ] / (49+81)

=(73+j)/130

=73/130+j/130

2. Looks right to me!

3. Thanks! I really had doubts about "z1 / (z1 -z2) = (4 - j5) / (4 - j5 +3 -j4) = (4-j5)/(7 - j9)"

I wasn't sure whether it was (4 - j5 + 3 - j4) or (4 - j5 + 3 +j4)

4. Originally Posted by Benji123
Hi all. Not sure whether this is correct or not and I would like some guidance! Thanks...

Given that z1 = 4-j5 and z2 = -3+j4, Find the compelx number z1/z1-z2 in its simplest form.
$\displaystyle \frac{z1}{z1-z2}=\frac{4-5j}{4-5j-(-3+4j)}$
$\displaystyle \frac{z1}{z1-z2}=\frac{4-5j}{4-5j+(3-4j)}$
$\displaystyle \frac{z1}{z1-z2}=\frac{4-5j}{7-9j}$

-- hope it'll help --

5. So do I need to rationalize it or leave it as 4-5j/7-9j? Thanks.

6. You rationalise it, yes. Your answer is good, do not worry

7. Thanks people