Simplifying Complex numbers DAY 1 January 31, 2017

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 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 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 January 31, 2017

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 1 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.