Complex Numbers

Complex Numbers

by JadeAnthony Dosdos

​Objectives:

​At the end of the lesson, students should be able to:

​

-Add, subtract, and multiply complex numbers.

​-Find complex solutions and zeroes.

​Core Concept:

​Core Concept:

​Two complex numbers a + b i and c + d i are equal if and only if a = c and b = d.

​Example:

​Find the values of x and y that satisfy the equation 2x - 7i = 10 + yi

​2x = 10

​

x =

​

​x = 5

​-7i = yi

​-7 = y

Multiple Choice

Find the values of x and y that satisfy the equation x + 3i = 9 - yi

• x = -9

  i = 3

• x = -9

  i = -3

• x = 9

  i = 3

• x = 9

  i = -3

​Core Concepts:

​Example:

​Add or subtract and write in standard form.

​1. (8-i) + (5 + 4i)

​

​= (8+5) + (-1+4)i

​= (13) + (3)i

​= 13 + 3i

​2. (7-6i) - (3-6i)

​

​= (7 - 3) + (-6 + 6)i

​= (4) + ( o ) i

​= 4

​3. 13 - (2 + 7i) + 5i

​

​= (13 - 2) + (-7 + 5)i

​= (11) + (-2)i

​= 11 - 2i

Multiple Choice

Add: ( 2 + 9i ) + (11 - i)

• -13 + 8i

• 13 + 8i

• 9 - 8i

• 13 + 10i

Multiple Choice

Subtract: (13 + 4i) - (8 + 4i)

• 21

• 5

• 21 + 8i

• 5 + 8i

Multiple Choice

Add or Subtract: 16 - (13 + 6i) + 8i

• 3 + 2i

• 3 + 14i

• 3 - 2i

• 3 - 14i

​Example:

​Multiply and write in a standard form.

​1. (9 -2i)(-4+7i)

​

​= (9)(-4) + (9)(7i) + (-2i)(-4) + (-2i)(7i)

​= (-36) + (63i) + (8i) + (-14i²)

​= -36 + 71i + (-14) (i²) note: i²= -1

​= -36 + 71i + (-14)(-1)

​= -36 + 71i + 14

​= -36 + 14 + 71i

​= -22 + 71i

​2. 4i(-6 + i)

​

​= (4i)(-6) + (4i)(i)

​= (-24i) + (4i²)

​= (-24i) + (4)(i²)

​= -24i + (4)(-1)

​= -24i + (-4)

​= -24i - 4

Multiple Choice

Multiply: (-3i)(10i)

• 30i²

• -30i²

• -30

• 30

Multiple Choice

Multiply: (1-2i)(-1 + i)

• -1 + 3i

• 1 + 3i

• -1 - 3i

• 1 - 3i

Poll

Do you have any questions?

• Yes

• No