Understanding Complex Numbers in Mathematics

Learn about complex numbers, including real and imaginary parts, operations with complex numbers, the imaginary unit, equality of complex numbers, and finding square roots of negative numbers. Explore how to define and use the imaginary unit, add, subtract, and multiply complex numbers, find complex solutions and zeros, and more.

• Mathematics
• Complex Numbers
• Imaginary Unit
• Operations
• Solutions

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1. Bellwork 1. 2.

2. Complex Numbers Section 3.2

3. In your study of mathematics, you have probably worked with only real numbers, which can be represented graphically on the real number line. In this lesson, the system of numbers is expanded to include imaginary numbers. The real numbers and imaginary numbers compose the set of complex numbers.

5. What You Will Learn Define and use the imaginary unit i. Add, subtract, and multiply complex numbers. Find complex solutions and zeros.

6. The Imaginary Unit ? (Take Note) To overcome this problem, mathematicians created an expanded system of numbers using the imaginary unit ?, defined as ?. Note that ??= ?. ? = The imaginary unit ? can be used to write the square root of any negative number.

7. Take Note

8. Finding Square Roots of Negative Numbers

9. Complex Number A complex number written in standard form is a number a + b ? where a and b are real numbers. The number a is the real part, and the number bi is the imaginary part. a + b ? If b 0, then a + b ? is an imaginary number. If a = 0 and b 0, then a + b ? is a pure imaginary number. The diagram shows how different types of complex numbers are related.

10. Equality of Two Complex Numbers (Take Note) Two complex numbers ? + ?? and ? + ?? are equal if and only if a = c and b = d. Find the values of x and y that satisfy the equation 2? 7? = 10 + ??.

11. Try you Practice packet 3.2 B side problem number: 5,7

12. Operation with Complex Number Take note

13. You Try Try you Practice packet 3.2 B side problem number:8,11

14. Try you Practice packet 3.2 B side problem number: 14, 15

15. Complex Solutions and Zeros Solving Quadratic Equations

16. Finding Zeros of a Quadratic Function Graph the function in your calculator