Question

If i = sq. root of -1 and a and b are non-zero real numbers, what is 1/ (a+bi) ?

Answer 1

Multiply by conjugate.

Answer 2

(a-bi)/(a-bi) right?

Answer 3

Yes.

Answer 4

Multiply by that.

Answer 5

I got something weird like this
(a-bi)/a^2-b^2i^2

Answer 6

In the answer choices, theres no i

Answer 7

That's not weird, just... cumbersome
\[\huge \frac{a-bi}{a^2-b^2i^2}\]But what is \(\Large i^2 = ?\)

Answer 8

oh i see... i^2=-1

Answer 9

So... it becomes...?

Answer 10

It is really really really really important to remember \(i^2=-1\) and \(i=\sqrt{-1}\)
It's the whole reason we multiply by conjugate.

Answer 11

(a-bi) / a^2+b^2

Answer 12

And you're done.

Answer 13

\[
\left(\frac{a}{a^2+b^2}\right) - \left(\frac{b}{a^2+b^2}\right)i
\]

Answer 14

huh?

Answer 15

He just separated the real part from the imaginary.

Answer 16

ok