Download presentation

1
**5-4 Complex Numbers (Day 1)**

Objective: CA 5.0 Students demonstrate knowledge of how real number and complex numbers are related both arithmetically and graphically.

2
**Not all quadratic equations have real number solutions.**

has no real number solutions because the square of any real number x is never negative.

3
To overcome this problem, mathematicians created an expanded system of numbers using the imaginary unit. The imaginary unit i can be used to write the square root of any negative number.

4
**The square root property of a negative number property**

1. If r is a positive real number then:

5
**2. By property (1): it follows that…**

6
Example 1: Solve

7
**If b 0 then a + bi is an imaginary number**

A complex number written in standard form is a number a + bi where a and b are real numbers. The number a is the real part of the complex number, the number bi is the imaginary part. If b 0 then a + bi is an imaginary number If a= 0 and b ≠ 0 then a + bi is a pure imaginary number.

8
**Every complex number corresponds to a point in the complex plane.**

Keep in mind: a is the real part (x –coordinate) bi is the imag. part (y-coordinate)

9
Example 2: 2-3i = (2, -3) -3+2i = (-3, 2) 4i = (0, 4)

10
**Difference of complex numbers**

Two complex numbers a + bi and c + di are equal if and only if a=c and b=d Sum of complex numbers Difference of complex numbers

11
Simplify: √-18 + √-32 i√18 + i√32 3i√2 + 4i√2 7i√2

12
**Example 3: Write the expression as a complex number in standard form.**

4 – i i 7 + i

13
Example 4: 7 – 5i i 6 + 0i 6

14
Example 5: i i -9i + 4i -5i

15
**Multiplying Complex Numbers**

To multiply complex numbers use the distributive property or the FOIL method.

16
**Example 5: Write each expression as a complex number in standard form.**

1.

17
Example 6:

18
Example 7:

19
**Homework= Accelerated Math Objective:**

Add & Subtract/Multiply Complex Numbers

Similar presentations

OK

5.9 Complex Numbers Objectives: 1.Add and Subtract complex numbers 2.Multiply and divide complex numbers.

5.9 Complex Numbers Objectives: 1.Add and Subtract complex numbers 2.Multiply and divide complex numbers.

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on weapons of mass destruction pictures Maths ppt on exponents and powers Ppt on reuse of waste material Ppt on web browser Ppt on limits and derivatives doc Ppt on rc phase shift oscillator derivation Ppt on storage devices-recent trends Ppt on boilers operations analyst Ppt on body language with pictures Ppt on nature and history of democracy in nepal