Download Complex Numbers 5-6

Algebra 2
Complex Numbers
Algebra 2
Square root of a negative numberFor any positive real number a,
For example:
–169 = 13i
-a = i
a
Complex Numbers
Lesson 5-6
Algebra 2
Additional Examples
Simplify
–54 =
=
–1 • 54
–1 •
=i•
54
=i•3
= 3i
6
6
54
–54 by using the imaginary number i.
Complex Numbers
Lesson 5-6
Algebra 2
Additional Examples
Write
–121 – 7 in a + bi (Complex Number) form.
–121 – 7 = 11i – 7
= –7 + 11i
Simplify the radical expression.
Write in the form a + bi.
Complex Numbers
Lesson 5-6
Algebra 2
Additional Examples
Simplify the expression (3 + 6i) – (4 – 8i).
(3 + 6i) – (4 – 8i) = 3 + (–4) + 6i + 8i
= –1 + 14i
Use commutative and
associative properties.
Simplify.
Complex Numbers
Lesson 5-6
Algebra 2
Additional Examples
Find each product.
a. (3i)(8i)
(3i)(8i) = 24i 2
Multiply the real numbers.
= 24(–1)
Substitute –1 for i 2.
= –24
Multiply.
b. (3 – 7i )(2 – 4i )
(3 – 7i )(2 – 4i ) = 6 – 14i – 12i + 28i 2
Multiply the binomials.
= 6 – 26i + 28(–1)
Substitute –1 for i 2.
= –22 – 26i
Simplify.