Imaginary Numbers ???Imaginary Numbers ???

In real life, complex numbers are used by engineers and physicists to measure electrical currents, to analyze stresses in structures such as bridges and buildings, and to study the flow of liquids.

Engineers who design speakers use complex numbers.

Engineers who design and test the strength of bridges use complex numbers.

Scientists who do experiments on ways to

make energy using fuel cells, batteries, and solar cells use complex numbers.

Complex numbers are also used for generating fractals, which are geometric objects created by making a repeating pattern.

Which is actually very useful Which is actually very useful because…because…

……by simply accepting that i exists by simply accepting that i exists lets us solve things where we need lets us solve things where we need

the square root of a negative the square root of a negative number.number.

Example: What is the square root of -25?

Answer:

i512525

A few questions…A few questions…

SimplifySimplify

A) A) B) B) 482 9

10 i ii 1 12 i ii 3

14 i ii 5 6i 7i8i 9i 10i 11i

Question 1Question 1

Question 2Question 2

Question 3Question 3

Question 4Question 4

Complex NumbersComplex Numbers

Complicated?

Try it!Try it!

+

Solve Solve

01062 xx

Graph it! Graph it! Can you solve it graphically?Can you solve it graphically?

What do you notice? What do you notice?

Solve Algebraically! Solve Algebraically!

01062 xx

Practice!Practice!Simplify.Simplify.

 a)    

b)

c)     

d)

e)        

f)  

4 16

8 184

1694 1510

Solve:Solve: