Math 15200 Lesson 13 Section 1.4 - Mixed Review Worksheet Page 3
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1
2
3
4
5Ex 3: Find each product in standard form.
a
)
4 (
−
5
i
)(
2
−
6
i
)
=
)
4 (
9
)(
2
36
)
b
+
−
−
−
−
=
2
c
)
4 (
−
7
i
)
=
d
)
6 (
−
i
2
)(
6
+
i
) 2
3
1
e
)
4
i
−
i
4
4
V
Complex Conjugates and Division of Complex Numbers
Remember the conjugate of
a
+
bi
is
a
−
bi
and vice-versa. The product of conjugates is
2
2
a −
b
. Because the square of a real number is always a rational number, the product of
two conjugates will be rational (without a radical). This product will help us divide
complex numbers. Multiply numerator and denominator by the conjugate of the
denominator, just like you did when rationalizing a fraction with a binomial denominator
containing a radical.
Ex 4: Divide and write answer in standard form.
12
a
)
=
3
i
3
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