Simplifying Complex numbers Day 1€¦ · Simplifying Complex numbers Day 1 December 07, 2017 Solve...
Transcript of Simplifying Complex numbers Day 1€¦ · Simplifying Complex numbers Day 1 December 07, 2017 Solve...
Simplifying Complex numbers Day 1 December 07, 2017
Solve by completing the square
Find the value that completes the square and rewrite as a perfect square binomial x2 + 8x + ____
Daily Quiz
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.
Objective:
NCN.1 i2=1 and a+bi Simplifying Complex number using algebraic properties
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)
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
.
Simplifying Complex numbers Day 1 December 07, 2017
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
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
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.