MATH 1310/8.7
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Transcript MATH 1310/8.7
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