Simplifying Complex numbers.notebook February 05, 2018
Find the discriminant. State number of solutions and type.
Warm up
Students will • know there is a complex number i such that i 2 = –1 and that every complex number has the form a+bi with a and b real. • simplify expressions by add and subtracting and multiplying complex numbers (a + bi) by using algebraic properties.
NCN.1Learning intention:
success criteria:1. I will be able to use distributive property to complex numbers.2. I will be able to combine like terms to simplify complex numbers.
imaginary number a term that has an i.
ex:
Vocabulary
Complex number the sum of a real number and an imaginary number. Has the general form a+bi.
ex:
a+bi(real part) (imaginary part)
Simplifying Complex numbers.notebook February 05, 2018
Example 1
steps Whya)
b)
Write as a multiple of i
• We can't have a negative number in a radical
√-1=i
• perfect squares come out of the square root
. Example 2
steps Whya)
b)
Write as a multiple of i
• We can't have a negative number in a radical
√-1=i
• perfect squares come out of the square root
.
Simplifying Complex numbers.notebook February 05, 2018
Simplify the following expressions.
a) b)
UTRY11
Example 3steps Why
a)
b)
simplify
• replace i2 with -1
• i2=-1
• even powers give us positive answers
Example 4steps Whysimplify
c) d)• replace i2 with -1
• i2=-1
• odd powers give us negative answers
Challenge problem. Simplify i355 explain how you got your answer in a complete sentence.
remember to use academic vocabulary in your sentences.
pair share
Simplifying Complex numbers.notebook February 05, 2018
Simplify the following expressions.
a) b)
UTRY13
Students will • simplify expressions by add and subtracting and multiplying complex numbers (a + bi) by using algebraic properties.
NCN.1Learning intention:
success criteria:1. I will be able to use distributive property to complex numbers.2. I will be able to combine like terms to simplify complex numbers.
Example 5 steps Why
a)
b)
simplify • we can only add real numbers with real number and imaginary numbers with imaginary.
• we must distribute the negative before adding like terms
• combine like terms
• combine like terms
What if we add (4 + 2i) to problem (b)
What would be our new answer explain.
pair share
remember to use academic vocabulary in your sentences.
Simplifying Complex numbers.notebook February 05, 2018
Example 5 steps Why
a)
b)
simplify • we can only add real numbers with real number and imaginary numbers with imaginary.
• we must distribute the negative before adding like terms
• combine like terms
• combine like terms
What if we add (4 + 2i) to problem (b)
What would be our new answer explain.
pair share
remember to use academic vocabulary in your sentences.
1. Add: (7 + 5i) + (8 3i) 2. Add: (2 + 3i) (8 6i)
Example
Example
a) b)
find the productExample 7
steps Why
a)
b)
simplify• the square of a term is multiplying the terms by it self
• we can only add real numbers with real number and imaginary numbers with imaginary.
(associative property)
• i2=-1
Explain how the i infront of the parenthesis changes the last step on example (a)
remember to use academic vocabulary in your sentences.
pair share