EM Fields (ECE3105 Fall 2024)
Instructor: Yong Xu
HW 1A (Due 09/04/2024, Wednesday)
•
Throughout this semester, we will typically limit phase angles of complex numbers to
within the range of −180° to 180°.
Problem 1 (3 pts each). Five complex numbers will be used in this assignment. Their values
are listed below:
𝐴 = −0.55 − 2𝑗, 𝐵 = 3 − 2𝑗, 𝐶 = 1.9∠35°, 𝐷 = 1.7𝑒 2𝑗 , and 𝐸 = 𝑒 0.5−2𝑗 .
Determine the values of the quantities listed below.
(a) The real part of D, i.e., 𝑅𝑒(𝐷); (Q1)
(b) The absolute value of A, i.e., |𝐴|; (Q2)
(c) The phase angle of A in degrees, i.e., ∠𝐴; (Q3)
(d) The real part of 𝐴⁄𝐵; (Q4)
(e) The absolute value of 𝐴⁄𝐵; (Q5)
(f) The phase angle of A/D in degrees; (Q6)
(g) The absolute value of (𝐴 + 𝐶)⁄(𝐵 + 𝐷); (Q7)
(h) The phase angle of (𝐴 + 𝐶)⁄(𝐵 + 𝐷); (Q8)
(i) The imaginary part of (𝐴 + 𝐶)⁄(𝐵 + 𝐷); (Q9)
𝐴
𝐶
(j) The absolute value of 𝐵 + 𝐷; (Q10)
(k) The phase angle of
𝐴
𝐶
+ ; (Q11)
𝐵
𝐷
(l) The absolute value of
1
+ 1.5𝐵; (Q12)
𝐸∗
Problem 2. (5 pts each) Consider two real vectors in rectangular coordinates: 𝐴⃗ = 2𝑒⃗𝑥 + 1.5𝑒⃗𝑦 −
⃗⃗ = 2𝑒⃗𝑥 − 5𝑒⃗𝑧 . Calculate:
3𝑒⃗𝑧 , 𝐵
⃗⃗; (Q13)
(a) 𝐴⃗ ∙ 𝐵
(b) The magnitude (i.e., length) of vector 𝐴⃗; (Q14)
(c) The angle between the vector A and the positive y axis. Express your result in degrees
and limit it within the range of 0 to 180 degrees. (Q15)
⃗⃗, i.e., |𝐴⃗ × 𝐵
⃗⃗| (Q16)
(d) The length of the vector cross-product 𝐴⃗ × 𝐵
⃗⃗) (Q17)
(e) The value of 𝑒⃗𝑥 ∙ (𝐴⃗ × 𝐵
(f) The angle between vector A and B. Express your result in degrees and limit it within the
range of 0 to 180 degrees. (Q18)