Download Alg II H notes 5.4

5.4 Complex Numbers
Students will be able to:
Solve quadratic equations with complex solutions.
Perform operations with complex numbers.
The square root of a negative number
Property
Example
1. If r is a positive real number,
Then
.
2. By the above property, it follows th
.
Example 1 Solving a Quadratic Equation.
Solve 3x² + 10 = -26
You Try.
Solve the equation.
1. x² = -9
2. 2x² + 3 = -13
A complex number written in standard form is a number a+bi where a
and b are real numbers. The number a is the real part of the the
imaginary number, and the bi is the imaginary part. If b≠0 then a + bi is
an imaginary number.
Example 2 Plotting imaginary numbers
Plot the complex numbers in the complex plane.
a. 2 – 3i
b. -3 + 2i
c. 4i
Example
3 Adding and Subtracting Complex Numbers
Write the expression as a complex number in standard form.
a. (4 – i) + (3 + 2i)
b. (7 – 5i) – (1 – 5i)
c. 6 – (-2 + 9i) + (-8 + 4i)
Example 4 Multiplying Complex Numbers
Write the expression as a complex number in standard form.
a. 5i(-2 + i)
b. (7 – 4i)(-1 + 2i)
c. (6 + 3i)(6 – 3i)
Example 5 Dividing Complex Numbers
Write the quotient in standard form:
You Try
Write the expressions as a complex number in standard form.
3. (1 + 5i) + (6 – 2i)
4.
5. (1 – i)(7 + 2i)
6.
(4 + 3i) – (-2 + 4i)