QUESTION 1 (50 marks total) (-5j) - j(j+3) (j-2)' a) Find the real and imaginary parts...
(10 pts) Calculate the following a) Find the real and imaginary parts of e 3+nj b) Find the real and imaginary parts of ez? c) Write in polar form: 1+j
For the complex number given as: z = a + bi / c+di where i = √−1 is the imaginary unit. The parameters are defined as a = √2, b = 0, c = 0.5 and d = −0.5. (a) Find the real and the imaginary parts of z, and then draw the Argand dia- gram. (Hint: Use the conjugate of the denominator.) 2.5 (b) Based on the Argand diagram, find the distance r of the complex number z from...
Questions. (20 pts.) a) Find the real part and imaginary part of the following complex numbers 1. jel- 2. (1 - 0260 3. b) Find polar form of the following numbers 31-3 9 Question 2. (20 pts.) a) Simplify (2< (5/7) (2<(")) 2 < (-1/6) b) Solve z+ + Z2 + 1 = 0
Q4: 3 marks each part Answer 2 parts from the following (a) Find the real and imaginary parts of each side of 1+a ei + az ezi® + ... = (1 - a el®)-1 (b) 2 Show that sin z cosh 2y-cos 2x (C) 1 Find the residues of at all its poles. e2z-ez
Real and Imaginary parts.
2. [10 marks Find all solutions to the equations 2 a) (b) e1. (24-1)sin(7T2) 0.
Need help for part(b) thx :)
Question 1: Find the real and imaginary parts, u and y, and the natural domain of (a) f(2)=z + (6) 9(2) = cc-*
Find the real and imaginary parts of the following (a) 3 /2 (b)c- (c) e3+12 (d)e-0-) (e)j
could use some help on these, will rate!
Find the real and imaginary parts of (2ei)' b) z= (2+3i)3 Problem 1.29 a) z= Problem 1.25 Light from a helium-neon laser has a wavelength of 633 nm and a wave speed of 3.00 x 10 m/s. Find the frequency, period, angular frequency, and wave number for this light.
Question 5 [15 marks] The complex numbers z and w are such that w = 1 + a, z =-b-, where a and b are real and positive. Given that wz 3-4, find the exact values of a and b. [7 marks] The complex numbers z and w are such that lz|-2, arg (z)--2T, lwl = 5, arg(w) = 4T. Find the exact values of i. The real part of z and the imaginary part of z ii. The modulus...
QUESTION 3 [12 MARKS Figure 3 shows a balanced Y-Y connection. It has a positive abe sequence. Given, Van = 240 sin(wt + 50°) V, 2 = 5+5j, and 2y = 15 + 15j. Find the following i) Total complex power at the source. 6109.2 L=135°VA ii) Total complex power at the load. 4581-72_450VA iii) Total complex power at the line. 1827 2450 VA iv) Line voltage. V 45.6 21-10V [12 Marks CO2, PO2, C3) N a V Z Z...