Unit 1 Intro Complex numbers i2=1 and a+biNOTES September 14, 2015
a)
b)
c)
Rewrite in exponential form
Rewrite in radical form
simplify
Daily Quiz Journal Prompta) Is this figure a square? Explain. Write a complete sentence.
remember to use academic vocabulary in your sentences.
Students will know there is a complex number i such that i 2 = –1and that every complex number has the form a+bi with a and b real.
Objective:
NCN.1 Unit 1: Complex numbers i2=1 and a+bi
imaginary number a term that has an i.
ex:
Vocabulary VocabularyComplex number the sum of a real number and an imaginary number. Has the general form a+bi.
ex:
a+bi(real part) (imaginary part)
Unit 1 Intro Complex numbers i2=1 and a+biNOTES September 14, 2015
(Write in a complete sentence using academic vocabulary)
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
.
Example 3steps Why
a)
b)
simplify
• replace i2 with -1
• i2=-1
• even powers give us positive answers
Unit 1 Intro Complex numbers i2=1 and a+biNOTES September 14, 2015
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
Closure
complex numbers
real numbers imaginary numbers
Write each number in its proper location in the Venn diagram
Example1A B
Simplify the following. Example2A B
Simplify the following.
Example3A B
Simplify the following. Example4A B
Simplify the following.
Unit 1 Intro Complex numbers i2=1 and a+biNOTES September 14, 2015
Example5A B
Simplify the following. Example6A B
Simplify the following.
Example7A B
Simplify the following.
