Complex Numbers

Inspired and base on Larsons Pre-Calculus textbook, Eight Edition. Published by Cengage Learning

Warm UpDo the following problems

Question: Find the solutions to the following quadratic equations

Warm Up AnswersQuestion: Find the solutions to the following quadratic equations

Warm Up Answers Cont.Question: Find the solutions to the following quadratic equations

Brief Introduction

This is a funny clip, Remember Student, imaginary unit i isnot hard to understand. Your head wont blow up.

Complex Number

Complex Number cont.

Complex Number Conjugate

Complex Number Conjugate Cont.

Operation with Complex Numbers

You remember how to add right?1+1 =2Do you remember how to subtract?5-2= 3You remember how to multiply right?4 *2 =8

Operation with Complex Numbers: Sum

Operation with Complex Numbers: Difference

Operation with Complex Numbers: Multiplying

Operation with Complex Numbers: Key Idea

When I add, subtract, or multiply a regular real number, I always get a real numbers in return. WOW real numbers are like complex numbers. You just learned to add, subtract, and multiply complex numbers.

Operation with Complex Numbers: Key Idea

Multiplying Conjugate

Question: How do I get just a real number form a complex number?Answer: multiply by its conjugate

Divide complex numbers

Divide complex numbers Cont.

You just learn how to use complex conjugates to write the quotient of two complex numbers in standard form.

Putting everything together, Complex solution of Quadratic Equation

Putting everything together, Complex solution of Quadratic Equation Cont. You just learned to find complex solutions of quadratic equation