EGN3420 University of South Florida Complex Numbers Homework Assignment 1 This homework better to be done by computer not hand written so I can print it an

EGN3420 University of South Florida Complex Numbers Homework Assignment 1 This homework better to be done by computer not hand written so I can print it and hand it out

the assignment is attached

1. Let k be an integer. Solve the following: (a) i 4k (b) i ?16k+3 (c) (i 5k?3 )(i ?k+1)

2. Solve each of the following equations for z: (a) 21 ? 5iz = 2zi (b) 49 + z 2 = 0 (c) z 2 = z(i ? 5) (d) z = (1 ? z)(1 ? 4i) (e) z 2 + zi + 12 = 0

3. Solve the linear system of equations: z1 + iz2 = ?1 z1 ? z2 = i

4. Draw plots for the regions described by the following equations: (a) iIm(z) < 3 (b) |z| = 1 + Im(z) (c) Re(z) > |z| + 3

5. Show that: Re(z) ? |z|.

6. Simplify the following expressions: (a) 1+i 3?3i (b) 1 5i (c) 4 1?i (d) 1+i ? 7 (1?i) 3 1

7. Write the following numbers in polar form (r, ?) and express ? in both Arg(z) and arg0(z) forms: (a) 4 + 3i (b) i ? 1 (c) ?1 ? i (d) ?i

8. Using the answers from Question 7, express the following in polar form: (a) 4+3i i?1 (b) (4 + 3i)(i ? 1)2 (c) (4 + 3i) ? i ? 1

9. Find all the three cube roots of i.

10. Find (1 ? i) 3 4 .

11. Solve the following quadratic equations: (a) z 2 + z + 1 = 0 (b) z 2 + zi + i = 0

12. Find the steady-state current, Is(t), in the following system. Given that, R = 10?, L = 10mH, C = 100µF and Vs(t) = 10cos(1000t). and see pic on the file attached EGN 3420 Homework Assignment 1 Complex Numbers
Dr. Nasir Ghani
September 2019
1. Let k be an integer. Solve the following:
(a) i4k
(b) i?16k+3
(c) (i5k?3 )(i?k+1 )
2. Solve each of the following equations for z:
(a) 21 ? 5iz = 2zi
(b) 49 + z 2 = 0
(c) z 2 = z(i ? 5)
(d) z = (1 ? z)(1 ? 4i)
(e) z 2 + zi + 12 = 0
3. Solve the linear system of equations:
z1 + iz2 = ?1
z1 ? z2 = i
4. Draw plots for the regions described by the following equations:
(a) iIm(z) < 3 (b) |z| = 1 + Im(z) (c) Re(z) > |z| + 3
5. Show that: Re(z) ? |z|.
6. Simplify the following expressions:
(a)
(b)
(c)
(d)
1+i
3?3i
1
5i
4
1?i
?
1+i 7
(1?i)3
1
7. Write the following numbers in polar form (r, ?) and express ? in both Arg(z) and arg0 (z)
forms:
(a) 4 + 3i
(b) i ? 1
(c) ?1 ? i
(d) ?i
8. Using the answers from Question 7, express the following in polar form:
(a)
4+3i
i?1
(b) (4 + 3i)(i ? 1)2
?
(c) (4 + 3i) i ? 1
9. Find all the three cube roots of i.
3
10. Find (1 ? i) 4 .
11. Solve the following quadratic equations:
(a) z 2 + z + 1 = 0
(b) z 2 + zi + i = 0
12. Find the steady-state current, Is (t), in the following system. Given that, R = 10?, L =
10mH, C = 100µF and Vs (t) = 10cos(1000t).
Figure 1: Figure for Question 12
2

Purchase answer to see full
attachment