Lesson Objectives Complex Numbers A complex Number is a combination of:

A Real Number

1 12.38 3/4 1998 -0.8625

And an Imaginary Number

Imaginary numbers are special because when squared they give a negative result. What are Complex

Numbers Complex numbers are used in many scientific and engineering fields including Physics, Chemistry, Biology, Mathematics and Statistics.

Complex Numbers are used to solve equations that could not be solved otherwise in the following fields:

Control Theory

Improper Integrals

Fluid Dynamics

Signal Analysis

Algebraic Number Theory

Analytic Number Theory Why use Complex Numbers? Examples

1 + i 39 +3i

o.8 - 2.2i A

complex number is a combination of a Real Number & an Imaginary Number To add two complex numbers we add each element separately Adding 1 + i

------- = ?

1 - i Examples To understand what complex numbers are.

To be able to simplify complex numbers

To be able to carry out simple calculations surrounding complex numbers. Solution

(1+i) (1+i)

------------ =

(1-i) (l+i)

1 + 2i - 1

----------- = i

1 + 1 The "unit" imaginary number (like 1 for real numbers) is i, which is the square root of -1

i x i = -1 Complex does

NOT

mean complicated (a+bi) + (c+di) = (a+c) + (b+d)i

Example:

(3+2i) + 1+7i) = (4+9i) Multiplying Each part of the first complex number is multiplied by each part of the second complex number Firsts: a.c Outers a.di

Inners: b1.c Lasts bi.di Example (3 + 2i) (1 + 7i) (3+2i) (1+7i) = 3xi + 3x7i + 2ix1 + 2ix7i)

= 3 + 21i + 2i + 14i

= 3 + 21i + 2i - 14

Because 1 = -1 Now who

wants to

play

BINGO How clever do

you feel

NOW

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