Completing the Square & Imaginary Numbers

Imagine

150

Evaluate: 

i^37

i

200

Solve for 'x' over the complex numbers.

(x+4)^2+16=0

-4+-4i

300

Write in the form a+bi

3+5i-(1-i)^2

3+7i

400

Write in the form a+bi

3i^5-4i^11+2i^3+10i^21+5i^400

5+15i

You Complete Me

150

What is the 'x' coordinate of the vertex of f(x)?

f(x)=x^2-8x+10

4

200

What is the 'x' coordinate of the vertex of f(x)?

f(x)=2x^2+5x+11

-5/4

300

Convert to vertex form:

f(x)=2x^2+3x+1

f(x)=2(x+3/4)^2-1/8

400

What values of 'b' make the solutions of the following equation imaginary?

x^2+2bx+5=0

-sqrt 5< b <sqrt 5

A Little Wordy

150

Find two numbers that have a sum of 10 and a product of 24. 

6 and 4

200

The area of a rectangle is 105. The length is one more than twice the width. Find the perimeter of the rectangle. 

Width = 7, Length = 15

300

A lemonade stand sells lemonade for $1 per cup. They currently average 50 sales per day. For every $0.25 increase in price, they expect to lose 5 customers per day. What price should they sell lemonade for to optimize income?

$1.75

400

A garden has dimensions of 10x20 meters. A uniform pathway will be placed around the garden such that the combined area of the pathway will be 100 square meters. What is the width of the pathway?

(5sqrt13 -15)/2 \approx1.51

Random (Not on Test)

150

Evaluate:

log_b(b^(x+3))=

x+3

200

Solve for 'x' over the complex numbers:

\frac{x+3}{x+2}=\frac{x+1}{x+4}

x=-2.5

300

Simplify the radical as much as possible:

\root{x}{x^(2x)*2^x

2x^2

400

Fully expand and simplify:

(2+i)^3

2+11i