Complex Numbers
 Numbers
that are not real are called
Imaginary. They use the letter i.
i
= √-1
or i2 = -1
Simplify each:
√-81
√-10
√-32
√-810

A
Complex Number is a number that has
both a Real and an Imaginary
component.
 Written in the form a + bi
a is the REAL number
 bi is the IMAGINARY number

 To
add, subtract, or multiply complex
numbers, just treat them like binomials.
 Don’t forget… i2 = -1
 1.
 2.
 3.
 4.
 5.
(6 + 4i) + (-2 – 2i)
(-14 + 2i) – (6 + i) + (19 + 10i)
(4i)(-7i)
(6 – 3i)(7 + 8i)
(5 – 3i)2
 Use
the CONJUGATE
 The conjugate of (a + bi) is (a – bi)
 The conjugate of (bi) is (-bi)
 Multiply
both the numerator and the
denominator by the complex conjugate
and simplify… write the answer as a + bi
 Remember: i2
= -1
1.
3.
6
7i
3+i
2–i
2.
3+i
3i
4.
5 – 6i
2 – 9i