1. ## Squares, complete the square, complex numbers, quadratic formula, discriminant

Test next week, need some help with my assignments.

First completing the square: $x^2-8x+32=0$
I've done it 4 different ways and I've deduced that it is either
$-4+8i, -4-8i$
$-4+4i, -4-4i$
$4+8i, 4-8i$
$4+4i, 4-4i$

Okay.. Second.. This needs to be written in standard form.
$\frac{8-7i}{3-4i}$

Third, and last for the moment. Solve the equation:
$-x^2+4=2x^2-5$

More to come once I get to them.

2. Idk number 2, but here're my attempts at one and 3:

1)

$(x-4)^2-4^2+32=0$
$
(x-4)^2=-16
$

$(x-4)= \sqrt{-16} = 4i$
$
x= 4+4i, x=4-4i
$

3)
$-x^2+4=2x^2-5$
$4=3x^2-5$
$9=3x^2$
$3=x^2$
$x=\sqrt{3}$

3. 2)
standar form is x+iy.

try multiplying the numerator and denominator of that expression by the conjugate of the denominator. the conjugate of a+ib is a-ib.