Download presentation

Presentation is loading. Please wait.

1
M.1 U.1 Complex Numbers

2
**What are imaginary numbers?**

Viewed the same way negative numbers once were How can you have less than zero? Numbers which square to give negative real numbers. “I dislike the term “imaginary number” — it was considered an insult, a slur, designed to hurt i‘s feelings. The number i is just as normal as other numbers, but the name “imaginary” stuck so we’ll use it.” Imaginary numbers deal with rotations, complex numbers deal with scaling and rotations simultaneously (we’ll discuss this further later in the week)

3
**Imaginary Numbers What is the square root of 9?**

4
Imaginary Numbers The constant, i, is defined as the square root of negative 1:

5
Imaginary Numbers The square root of -9 is an imaginary number...

6
Imaginary Numbers Simplify these radicals: =6xi =2y√5yi

7
Multiples of i Consider multiplying two imaginary numbers: So...

8
Multiples of i Powers of i:

9
Powers of i - Practice i28 i75 i113 i86 i1089 1 -i i -1

10
Solutions Involving i Solve:

11
**Complex Numbers Have a real and imaginary part .**

Write complex numbers as a + bi Examples: 3 - 7i, i, -4i, 5 + 2i Real = a Imaginary = bi

12
Add & Subtract Like Terms Example: (3 + 4i) + (-5 - 2i) = -2 + 2i

13
**Practice (4 + 7i) - (2 - 3i) (3 - i) + (7i) (-3 + 2i) - (-3 + i)**

Add these Complex Numbers: (4 + 7i) - (2 - 3i) (3 - i) + (7i) (-3 + 2i) - (-3 + i) = 2 +10i = 3 + 6i = i

14
Multiplying FOIL and replace i2 with -1:

15
Practice Multiply: 5i(3 - 4i) (7 - 4i)(7 + 4i) = i = 65

16
**Division/Standard Form**

A complex number is in standard form when there is no i in the denominator. Rationalize any fraction with i in the denominator. Monomial Denominator: Binomial Denominator:

17
Rationalizing Monomial: multiply the top & bottom by i.

18
**Complex #: Rationalize**

Binomial: multiply the numerator and denominator by the conjugate of the denominator ... conjugate is formed by negating the imaginary term of a binomial

20
Practice Simplify:

21
**Absolute Value of Complex Numbers**

Absolute Value is a numbers distance from zero on the coordinate plane. a = x-axis b = y axis Distance from the origin (0,0) = |z| = √x2+y2 Modulus

22
**Graphing Complex Numbers**

23
**Exit Ticket Simplify Write the following in standard form**

(-2+4i) –(3+9i) Write the following in standard form 8+7i 3+4i Find the absolute value 4-5i

24
Check Your Answers

25
**Homework Complex Numbers worksheet**

For #7, remember the quadratic formula!

Similar presentations

Presentation is loading. Please wait....

OK

Simplify each expression.

Simplify each expression.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on air powered vehicle Ppt on english speaking course Ppt on rbi reforms for the completion Ppt on male reproductive system of human Ppt on life cycle of silk moth Ppt on political parties and electoral process in india Ppt on anticancer therapy Ppt on total parenteral nutrition complications Ppt on articles of association for social clubs Download ppt on multimedia and animation