Download ALGEBRA 2 5.9: Operations with Complex Numbers

ALGEBRA 2
5.9: Operations with Complex
Numbers
Complex Plane
• x-axis is used as the real axis
• y-axis is used as the imaginary axis
W = 2 + 3i
V = -1 + 2i
3i
2i
1i
-1i
-2i
Example 1: Graph each complex number.
A = 2 – 3i
B = -1 + 4i
C = 4 + 5i
D = -5i
C
B
3i
2i
1i
-1i
-2i
A
D
Absolute Value
Distance a point is away from 0 on the complex plane
|4+2i|
3i
2i
1i
-1i
-2i
a  bi  a  b
2
2
Ex 2: Find each absolute value
A) |3 + 5i|
B) |-13|
C) |-7i|
Add or Subtract Complex Numbers
• Add like terms
• When you subtract, you need to distribute the
negative and then add like terms
Ex 4: Add or subtract. Write the result in the form a+bi.
A) (4 + 2i) + (-6 – 7i)
B) (5 – 2i) – (-2 – 3i)
C) (1 – 3i) + (-1 + 3i)
Multiply Complex Numbers
• Multiply (can use distributive or FOIL)
• Remember i2 = -1
• Add like terms
Ex 5: Multiply. Write the result in the form a+bi.
A) -2i(2 – 4i)
B) (3 + 6i)(4 – i)
C) (2 + 9i)(2 – 9i)
D) (-5i)(6i)
Powers of i
i=
i5 =
i2 =
i6 =
i3 =
i7 =
i4 =
i8 =
Rule:
i9 =
i10 =
i11 =
i12 =
Ex 6: Simplify.
A) - 6i14
B) i63
Divide Complex Numbers
• Cannot have an i on the bottom
• Rationalize by multiply top and bottom by complex conjugate
of bottom.
• Ex 7:
A) 3  10i
5i
B) 2  8i
4  2i
Assignment #9 Page 386 #’s 3674,(122)