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

• Dec 21st 2009, 03:59 PM
jscalalamoboy
Squares, complete the square, complex numbers, quadratic formula, discriminant
Test next week, need some help with my assignments.

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

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

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

More to come once I get to them.
• Dec 21st 2009, 04:08 PM
Quacky
Idk number 2, but here're my attempts at one and 3:

1)
http://www.mathhelpforum.com/math-he...9808466e-1.gif
$\displaystyle (x-4)^2-4^2+32=0$
$\displaystyle (x-4)^2=-16$
$\displaystyle (x-4)= \sqrt{-16} = 4i$
$\displaystyle x= 4+4i, x=4-4i$

3)
$\displaystyle -x^2+4=2x^2-5$
$\displaystyle 4=3x^2-5$
$\displaystyle 9=3x^2$
$\displaystyle 3=x^2$
$\displaystyle x=\sqrt{3}$
• Dec 21st 2009, 07:39 PM
Krahl
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.