Complex numbers CONTRADICTION? (1 Viewer)

[zando6]

hey guys
1. I proved that z^-1=conj z, converting into mod-arg form and by doing de moivres theorem so this must therefore be true
1/(2+3i)=2-3i

2. yet when i substituted z for an actual complex number eg. z=2+3i
and then did the realisation the answer is different
1/(2+3i) X (2-3i)/(2-3i)=(2-3i)/13

3. and i learned of a complex number rule where
z^-1=conj z/(mod z)^2
and this rule is consistent with what got ... which was (2-3i)/13

so now the question finally is why are there 2 answers that seem right?

 

[deterministic]

1/z=conj(z) only holds if mod(z)=|z|=1
otherwise 1/z= conj(z)/|z|^2

 

[ohexploitable]

 

[zando6]

ok thanks, i get it now.

 

[Pwnage101]

Edited, thanks to Drongoski for picking up the typo.

 

[Drongoski]

shouldn't the + be - ?

 

[Aquawhite]

shouldn't the + be - ?

I believe so, he's just made a little typo there.

 

[Drongoski]

Pwnage101 made a good observation of a slip but made one himself. I'm not faulting him - just that it is so easy to make one, e.g. a typo.

 

[Pwnage101]

True. Thanks for that Drongoski. Lesson learned: don't be lazy and copy the LaTeX code from other people, and if you do make sure you have the right line.