Question

Multiplying with complex numbers?

Answer 1

Have to type out the problem, one second!

Answer 2

Find a polynomial with real coefficients that has the following zeros:
\[-1 - \sqrt{3}i\], 3, -1
Now I know there has to be a conjugant of \[-1 - \sqrt{3}i\] so the other zero is \[-1 + \sqrt{3}i\]

So I got \[(x + 1)(x - 3)(x + 1 + \sqrt{3}i)(x + 1 - \sqrt{3}i)\]
So now:
(\[(x ^{2} - 2x - 3)(x + 1 + \sqrt{3}i)(x + 1 - \sqrt{3}i)\]

I know (a + bi)(a - bi) = a^2 + b^2, but I would like to know how to do it out long hand

Answer 3

if you expand

(a+bi)(a-bi) = a^2-abi+abi-b^2i^2

abi cancels (and i^2 is just -1)
and you are left with
=a^2-(-b^2) = a^2+b^2

Answer 4

Ohh!! Okay. Thank you!

Answer 5

yw