Complex Numbers(Not that hard)

5.9

An Equation with “No Solutions”?

• Suppose you were told that the sum of two and twice the square of a number is zero. What number(s) satisfy those conditions?

• Write an equation:

• Factor out a 2

• Divide out 2

• Isolate and take the square root.

• So, would most of you say there is no solution?

Real World Uses of Complex Numbers

Complex numbers are used a great deal in electronics. The main reason for this is they make the whole topic of analyzing and understanding alternating signals much easier. This seems odd at first, as the concept of using a mix of real and 'imaginary' numbers to explain things in the real world seem crazy! Once you get used to them, however, they do make a lot of things clearer. The problem is understanding what they 'mean' and how to use them in the first place.http://www.st-andrews.ac.uk/~www_pa/Scots_Guide/info/signals/complex/cmplx.html

Imaginary Unit

Pure Imaginary Number,where b is any real number

Simplifying Square Roots of Negative Numbers

Simplifying with Pure Imaginary Numbers

Powers of

Solving Equations with Imaginary Solutions

Complex Number System

Understanding the Relationship between Number Types

Complex Number System

Real Numbersb=0

Imaginary Numbers

Pure Imaginary Numbersa = 0

Equal Complex Numbers

• For two complex numbers to be equal, the real and imaginary parts must be equal.

• Find the values of that make the equation

Equating Complex Numbers

• Find the values of that make the equation

Adding and Subtracting Complex Numbers

• Add the real and imaginary parts.

Multiply Complex Numbers

• Use FOIL, change any to -1, then simplify.• In an AC circuit, the voltage E, current I, and

impedence Z are related by the formula . Find the voltage in a circuit with current amps and impedence ohms. *Electrical engineers use j for the imaginary unit to avoid confusion with the I for current.

• volts

Divide Complex Numbers

Assignment

• P. 274;42-62 all