Test Review - U5A Complex Numbers and Solving Quadratics

Simplify

100

i¹⁵³

i

200

14i¹²⁷

14i

300

21i¹⁰+6i³¹

-21-6i

400

 3sqrt(-108) 

18isqrt3

500

 4sqrt(-24) +2sqrt(-96) 

16isqrt6

Operations with Complex Numbers

100

Find the product of (2+3i) and (3+6i)

-12+21i

200

Find the sum of (12+7i) and (5-3i)

17+4i

300

Subtract (15+11i) from (50-6i)

35-17i

400

Subtract (3+2i) from (9-7i)

6-9i

500

Divide (8+9i) by (1-7i)

-11/10+(13i)/10

Solving Quadratics

100

x²+50=0

x = ±5i√2

200

x²-6x=-12

x = 3+-isqrt3

300

-x² = -7x+18

x = 7/2 +- (isqrt23)/2

400

3x²+15x=-27

x=-5/2+-(isqrt11)/2

500

5x²+ 6 = 4x

x=2/5 +- (isqrt26)/5

Solve Inequalities(Answers in interval notation)

100

Solve inequality

 x^2-3x<=4 

[-1, 4]

200

Solve inequality 

 -x^2-5x+6>0 

(-6,1)

300

Solve inequality 

 -8x^2-1<=-6x 

(-oo,1/4]uu[1/2,oo) or (-oo,0.25]uu[0.5,oo)

400

Solve inequality  4x^2-12>3x^2+x 

(-oo-3)uu(4,oo)

500

Solve inequality 

 3x^2-x>=4x^2+6 

no solution

Solve Systems of Equations (real only)

100

Solve  

{(y,=,2x),(y,=,x^2):} 

(0,0), (2,4)

200

Solve  {(y=x^2-2x-3),(y=-x-1):} 

(-1,0) and (2,-3)

300

Solve  {(y = 2x^2 -3x + 4),(y = x + 2):} 

(1,3)

400

Solve 

{(y = 2x),(x^2 + y^2 = 10):}

(-sqrt2,-2sqrt2), (sqrt2, 2sqrt2)

500

Solve  {(y^2,=,3x,-,1),(x^2,+,y^2,=,9):}

 (2,-sqrt5) or (2,sqrt5) 

Mixed Bag

100

What is the conjugate of 6i - 9

-9-6i 

*has to be in a+bi form

200

Solve 4x² + 16 = 0

x=+-2i

300

Simplify  -3i^21+4i^18 

-4-3i

400

Simplify 2(3-4i)-5(2+7i)+(8-12i)

4-55i

500

Simplify  4sqrt(-108) 

24isqrt3