A.6 Complex Numbers & Solving Equations

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A.6 Complex Numbers & Solving Equations

Presentation transcript:

A.6 Complex Numbers & Solving Equations It is our choices…who show who we really are, far more than our abilities. -Albus Dumbledore

Solving Equations Let’s recall solving the following equation. If we extend our number system to include complex numbers, we can solve the previous equation. How cool is that! If N is a positive real number, we define the principal square root of –N, denoted by , as

In Complex Number System Evaluate the square root of the following negative numbers in the complex number system. 1) 2)

Equations in Complex Number System Solve the following equations in the complex number system.

Equations in Complex Number System Solve the following equations in the complex number system.

Equations in Complex Number System Now that we have extended our number system to include complex numbers, we should get as many solutions as the degree of the polynomial we are trying to solve!

Character of Solutions For the equation the equation has two unequal real solutions the equation has a repeated real solution the equation has two complex solutions that are not real and are conjugates of each other Now look at your worksheet for determining the character of the equations!

A.6 Complex Numbers & Solving Equations STUDY GUIDE DUE MONDAY!! Challenge Problem Due Tuesday Homework #9: p.1008 #55 – 71 EOO, 73 It is our choices…who show who we really are, far more than our abilities. -Albus Dumbledore