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.
Q5B. Find the type of the controller in the following figures and use real values to find the transfer
function of three of them[ Hint Pi,Pd and Lead,lag are found so put the controller with its
corresponding compensator].
R₁
R₂
Rz
HE
C2
RA
HE
R₁
R2
RA
と
Q1// Sketch the root locus for the unity feedback system. Where
G(s)=)=
K
S3+252 +25
and find the following
a. Sketch the asymptotes
b. The exact point and gain where the locus crosses the jo-axis
c. The breakaway point on the real axis
d. The range of K within which the system is stable
e. Angles of departure and arrival.
Determine X(w) for the given function shown in Figure (1) by applying the
differentiation property of the Fourier Transform.
Figure (1)
-1
x(t)
Chapter 2 Solutions
Power System Analysis and Design (MindTap Course List)
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