Given the complex numbers A 1 = 6 ∠ 30 and A 2 = 4 + j 5 , (a) convert A 1 to rectangular form: (b) convert A 2 to polar and exponential form: (c) calculate A 3 = ( A 1 + A 2 ) , giving your answer in polar form: (d) calculate A 4 = A 1 A 2 , giving your answer in rectangular form: (e) calculate A 5 = A 1 / ( A 2 * ) giving your answer in exponential form.
Given the complex numbers A 1 = 6 ∠ 30 and A 2 = 4 + j 5 , (a) convert A 1 to rectangular form: (b) convert A 2 to polar and exponential form: (c) calculate A 3 = ( A 1 + A 2 ) , giving your answer in polar form: (d) calculate A 4 = A 1 A 2 , giving your answer in rectangular form: (e) calculate A 5 = A 1 / ( A 2 * ) giving your answer in exponential form.
Solution Summary: The author explains the rectangular form of a complex number A_1 and the exponential and polar forms of complex numbers.
Given the complex numbers
A
1
=
6
∠
30
and
A
2
=
4
+
j
5
, (a) convert
A
1
to rectangular form: (b) convert
A
2
to polar and exponential form: (c) calculate
A
3
=
(
A
1
+
A
2
)
, giving your answer in polar form: (d) calculate
A
4
=
A
1
A
2
, giving your answer in rectangular form: (e) calculate
A
5
=
A
1
/
(
A
2
*
)
giving your answer in exponential form.
(a) Determine the value of Z, in the circuit of Figure Q3(a) for maximum power
transfer.
Practice Exercise 1.1
Answer the following accordingly:
1. (3-j4) + (10244) then convert to
rectangular form
2. (22000+j13)/(32-17) then convert to
rectangular form
3. Convert 95-j12 to polar form
Find the impedance Zab in the circuit seen in figure. Suppose that R = = 4.5 2.
Part A
Zab =
Part B
Ω
Zab
Zab
R
ww
Ω
-182
카
ZAN
20
M
Express Zab in polar form.
Express your answer in ohms to three significant figures. Enter your answer using angle notation. Express
argument in degrees.
ANSWER:
40 0
Express Zab in rectangular form.
Express your answer in ohms to three significant figures. Enter your answer in rectangular form.
ANSWER:
m
102
-/200
j200
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