Polar Coordinates And Complex Numbers Worksheets With Answers - Math 611b Page 20
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50Complex Numbers in Polar Form Worksheet (9.6)
1. Explain how to find the absolute value of a complex number.
2. Write the polar form of i.
3. Solve each equation for x and y, where x and y are real numbers.
a) 2x + y + yi = 5 + 4i
b) 1 + (x + y)i = y + 3xi
4. Graph each number in the complex plane and find its absolute value.
+
a) ! 2 ! i
d) ! 1 ! 5i
1
2
i
b)
c) 2 + 3i
− +
1
5i
e)
5. Express each complex number in polar form.
− −
−4 2
c) ! 4 + i
d) ! 2 + 4i
1
3i
a) 4 + 5i
b)
e)
6. Graph each complex number. Then express it in rectangular form.
π
π
π
π
3
π
π
+ i
+ i
+ i
4
(cos
sin
)
(cos
2
sin
2
)
3
(cos
sin
)
a)
b)
c)
3
3
2
4
4
π
π
π
π
4
4
5
5
+ i
+ i
+ i
2
(cos
sin
)
2
(cos
sin
)
5
(cos
0
sin )
0
d)
e)
f)
3
3
4
4
+ j
10
(cos .
0 7
sin . )
0 7
7. A series circuit contains two sources of impedance, one of
ohms and the
+ j
16
(cos .
0 5
sin . )
0 5
other of
. (Note: j is used by engineers in place of i.)
a) Convert these complex number to rectangular form.
b) Add your answers from part a to find the total impedance in the circuit.
c) Convert the total impedance back to polar form.
20
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