What is the additive inverse and multiplicative inverse of 3-i ? Can someone explain to me what those are please?

Question

helder_edwin · Answer

the additive inverse of x is -x.
the multiplicative inverse of $x\neq0$ is 1/x

helder_edwin · Answer

so for instance. if $z=-3+4i$, then $-z=3-4i$ is the additive inverse of z.

since $z=-3+4i\neq0$ then its multiplicative inverse is
$$ \large z^{-1}=\frac{1}{-3+4i}\cdot\frac{-3-4i}{-3-4i}=\frac{-3-4i}{9+16}=
   \frac{-3-4i}{25}=-\frac{3}{25}-\frac{4}{25}i $$

3psilon · Answer

why do we multiply by the conjugate again @helder_edwin ?

3psilon · Answer

I get everything else I just forgot that concept

helder_edwin · Answer

it is a "shortcut" to do division with complex numbers.

3psilon · Answer

Ohh okay okay thank you so much!