Algebra 2 Final Review Game #3

Complex Numbers

100

i^38

i^38=i^36cdoti^2=(1)cdot(-1)=-1

200

(3+4i)(2-i)

6-3i+8i-4i^2

6+5i-4(-1)

6+5i+4

10+5i

300

3/(5-3i)

3/((5-3i))cdot((5+3i))/((5+3i))=(15+9i)/(25-9i^2)=(15+9i)/(25-9(-1))

=(15+9i)/(25+9)=(15+9i)/34

=15/34+9i/34

Quadratics

100

"Solve "x^2+9=0

x^2=-9

sqrt(x^2)=pmsqrt(-9)

x=pm3i

200

"Solve  "3x^2-x+3=0

x=(-bpmsqrt(b^2-4ac))/(2a)" "implies" "x=(1pmsqrt(1-4(3)(3)))/(2(3))

x=(1pmsqrt(-35))/6=(1pmsqrt(35)i)/6

x=1/6pmsqrt(35)/6i

Rational Expressions

100

(x^2+15x+56)/(x^2+7x)div(x^2-64)/(2x+16)

(x^2+15x+56)/(x^2+7x)cdot(2x+16)/(x^2-64)

((x+7)(x+8))/(x(x+7))cdot(2(x+8))/((x+8)(x-8))

(2(x+8))/(x(x-8))

200

2/(5a)+4/(3b)

2/(5a)cdot((3b))/((3b))+4/(3b)cdot((5a))/((5a))

=(6b)/(15ab)+(20a)/(15ab)=(6b+20a)/(15ab)

Rational Equations

100

3/(x+2)=5/x

3/((x+2))cdot((x)(x+2))/1=5/xcdot((x)(x+2))/1

3x=5(x+2)" "implies" "3x=5x+10" "implies" "-2x=10

x=-5

200

1/(2x^2)+3/(10x)=1/x-1/(5x^2)

(1(10x^2))/(2x^2)+(3(10x^2))/(10x)=(1(10x^2))/x-(1(10x^2))/(5x^2)

5+3x=10x-2" "implies" "7x=7

x=1