Polar Form Of Complex Numbers Worksheet With Answer Key - Openstax College Page 9
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25OpenStax-CNX module: m49408
9
θ
Find the angle
using the formula:
x
cos θ =
r
4
cos θ =
4 2
(10)
1
cos θ =
2
1
1
3π
θ = cos
=
4
2
3π
4 2
.
Thus, the solution is
cis
4
try it feature:
Exercise 10
(Solution on p. 18.)
z =
3 + i
Write
in polar form.
4 Converting a Complex Number from Polar to Rectangular Form
Converting a complex number from polar form to rectangular form is a matter of evaluating what is given and
z = r (cos θ + isin θ) ,
using the distributive property. In other words, given
rst evaluate the trigonometric
cos θ
sin θ.
r.
functions
and
Then, multiply through by
Example 6
Converting from Polar to Rectangular Form
Convert the polar form of the given complex number to rectangular form:
π
π
z = 12 cos
+ isin
(11)
6
6
Solution
We begin by evaluating the trigonometric expressions.
π
3
π
1
cos
=
sin
=
and
(12)
6
2
6
2
After substitution, the complex number is
3
1
z = 12
+
i
(13)
2
2
We apply the distributive property:
3
1
z = 12
+
i
2
2
3
1
(14)
= (12)
+ (12)
i
2
2
= 6 3 + 6i
6 3 + 6i.
The rectangular form of the given point in complex form is
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