lesson 2.4 read: pages 139-143 page 137: #1-73 (eoo)
TRANSCRIPT
Lesson 2.4
Read: Pages 139-143
Page 137: #1-73 (EOO)
Complex Numbers
Objectives
Students will use the imaginary unit i to write complex numbers, add subtract and multiply complex numbers, use complex conjugates to write the quotient of two complex numbers in standard form, and plot complex numbers in the complex plane.
abi
The Imaginary Unit
1i
𝑖2=−1
The set of real numbers is a subset of complex numbers.
RealNumbers
ImaginaryNumbers
ComplexNumbers
Addition and Subtraction of Complex Numbers
If are two complex numbers written in standard form, their sum and difference are defined as follows.
Sum: (a + bi) + (c + di) = (a + c) + (b + d)i
Difference: (a + bi) - (c + di) = (a - c) + (b - d)i
)32()3( ii
)5()32(3 ii
Perform the indicated operation.
444
Multiplying Complex Numbers
= (2i)(4i)
= 8
= 8
= -8
= 8 + 6i - 4i -3
= 8 + 6i - 4i -3
= 8 + 3 + 6i - 4i
= 11 + 2i
Complex Conjugates
(3 + 2i)(3 – 2i) = 9 - 6i + 6i -4
= 9 – 4(-1)
= 9 + 4
= 13
The product of two complex numbers can be a real number. This occurs with pairs of numbers of the forms a + bi and a – bi, called complex conjugates
Plotting Complex Numbers
The Complex Number Plane
Plot each number in the Complex Number Plane
a. -4 + 2i
b. 2 – 3i
c. 3 or 3 + 0i
d. 4i or 0 + 4i
e. 3 + 4i