Complex Numbers Worksheet Page 2
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2
3
4Example 2: Add: (2 – 3i) + (-4 + 5i)
Example 3: Subtract: (2 – 3i) – (-4 + 5i)
Example 4: Multiply: (2 – 3i)(-4 + 5i)
2
2
Recall: (a + b) and (a – b) are c onjugates. Therefore, (a + b)(a – b) = a
– b
.
a +
bi
and
a −
bi
are called complex conjugates therefore:
(
a
+
bi
)(
a
−
bi
)
=
2
−
3
i
Example 5 (Division): Simplify
(Hint: Multiply numerator and denominator by conjugate
−
4
+
5
i
of the denominator.)
Example 6 (Division): Find the reciprocal of 4 + 3i.
Page 2 (Section 1.5)
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