ECE 2000 Homework Set # 9 Name:_________________________
Spring 2004 Due by 4:00 PM on 5/7/04 Grade:_________
°
−
=
=
=
+
−=
30
4
1.1
3
2
2
1
250
17
79
300200
j
j
j
ez
ez
ez
jz
z
5
=
−
47
−
j31
z6=91ej0
z7=171ej
π
z8=312e−j
π
2
(note: All angles are in radians unless otherwise noted.)
Using the complex numbers given above, perform the computations by hand (without using the
complex number functions of a calculator) for the problems below. Show all your work. Perform all
additions and subtractions in rectangular form. Perform all multiplications, divisions, powers, and
roots in polar form.
Express your final answer in both rectangular form:
z
0
=
σ
+
j
ω
and in polar form ( with the angle in radians in the following interval
−
π
<
θ
≤+
π
): z0
=
re
j
θ
You should check your calculations using a calculator or Matlab®.
Problem 1. z
2110 zz +=
Problem 2. z
3111 zz −=
Problem 3. z
5412 zz=
Problem 4.
2
6
13 z
z
=z
Problem 5.
5
3
*
1
814 z
zz
z=z (Note: that term is the conjugate of )
*
1
z1
z
Problem 6. z
()
3
5115 zz +=
Problem 7. 3
7216 zz +=z (Note: give all 3 answers)