9.7 PRODUCTS AND QUOTIENTS OF COMPLEX NUMBERS IN POLAR FORMBy the end of this section students will be able to multiply and divide complex numbers in polar form as evidenced by a pair share activity.

Products and quotients of complex numbers in Rectangular form

By the end of the section students will be able to simplify complex numbers, graph complex numbers and convert complex numbers from polar to rectangular form and vice versa as evidenced by an exit slip.

𝒄 𝒅𝒊𝒂𝒃𝒊

𝑎𝑐𝑏𝑐 𝒊

𝑎𝑑 𝒊𝑏𝑑 𝒊𝟐

Real parts

Imaginary parts

Products of Complex numbers in Polar Form

**You will NOT be given this formula

By the end of this section students will be able to multiply and divide complex numbers in polar form as evidenced by a pair share activity.

Quotients of Complex numbers in Polar Form

• The process is similar but we need to use the conjugate and multiple top and bottom by

**You will NOT be given this formula

By the end of this section students will be able to multiply and divide complex numbers in polar form as evidenced by a pair share activity.

Example 1: Find the product/quotient, then express in polar and rectangular formA.

By the end of this section students will be able to multiply and divide complex numbers in polar form as evidenced by a pair share activity.

𝒓𝟏 ∙𝒓 𝟐𝒄𝒊𝒔 (𝜽¿¿𝟏+𝜽𝟐)¿𝒓𝟏

𝒓𝟐𝒄𝒊𝒔 (𝜽¿¿𝟏−𝜽𝟐)¿

−1

√3 260 °

B.

C.

By the end of this section students will be able to multiply and divide complex numbers in polar form as evidenced by a pair share activity.

𝒓𝟏 ∙𝒓 𝟐𝒄𝒊𝒔 (𝜽¿¿𝟏+𝜽𝟐)¿

−1√3

230 °

√2−√2

245 °

Example 1: Find the product/quotient, then express in polar and rectangular form

𝒓𝟏

𝒓𝟐𝒄𝒊𝒔 (𝜽¿¿𝟏−𝜽𝟐)¿

D.

E.

By the end of this section students will be able to multiply and divide complex numbers in polar form as evidenced by a pair share activity.

𝒓𝟏 ∙𝒓 𝟐𝒄𝒊𝒔 (𝜽¿¿𝟏+𝜽𝟐)¿

−1

√3 260 °

√2√22

45 °

Example 1: Find the product/quotient, then express in polar and rectangular form

𝒓𝟏

𝒓𝟐𝒄𝒊𝒔 (𝜽¿¿𝟏−𝜽𝟐)¿

F.

G.

By the end of this section students will be able to multiply and divide complex numbers in polar form as evidenced by a pair share activity.

𝒓𝟏 ∙𝒓 𝟐𝒄𝒊𝒔 (𝜽¿¿𝟏+𝜽𝟐)¿Example 1: Find the product/quotient, then express in polar and rectangular form

𝒓𝟏

𝒓𝟐𝒄𝒊𝒔 (𝜽¿¿𝟏−𝜽𝟐)¿

H.

I.

By the end of this section students will be able to multiply and divide complex numbers in polar form as evidenced by a pair share activity.

𝒓𝟏 ∙𝒓 𝟐𝒄𝒊𝒔 (𝜽¿¿𝟏+𝜽𝟐)¿

√2−√2

245 °

−1−√3

230 °

Example 1: Find the product/quotient, then express in polar and rectangular form

𝒓𝟏

𝒓𝟐𝒄𝒊𝒔 (𝜽¿¿𝟏−𝜽𝟐)¿

Summary1. Find the product and write in polar form AND

rectangular form: 2. Find the quotient and write in polar form AND

rectangular form:

By the end of this section students will be able to multiply and divide complex numbers in polar form as evidenced by a pair share activity.

Summary1. Find the product and write in polar form AND

rectangular form:

2. Find the quotient and write in polar form AND rectangular form:

By the end of this section students will be able to multiply and divide complex numbers in polar form as evidenced by a pair share activity.

By the end of this section students will be able to multiply and divide complex numbers in polar form as evidenced by a pair share activity.