Question

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

Answer 1

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

Answer 2

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
\[ \large z^{-1}=\frac{1}{-3+4i}\cdot\frac{-3-4i}{-3-4i}=\frac{-3-4i}{9+16}=
\frac{-3-4i}{25}=-\frac{3}{25}-\frac{4}{25}i \]

Answer 3

why do we multiply by the conjugate again @helder_edwin ?

Answer 4

I get everything else I just forgot that concept

Answer 5

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

Answer 6

Ohh okay okay thank you so much!