I. Given Z-2- i and Z2-1 2i. Find the following and express your answer in the...
and z2 = 1 1 + 3i 3-i a) Given that zı = find z such that z = 2 + i 4- ¿ 22 Give your answer in the form of a + bi. Hence, find the modulus and argument of z, such that -- < arg(2) < 7. (6 marks) b) Given w = = -32, i. express w in polar form. (1 marks) ii. find all the roots of 2b = -32 in the form of a...
| 1. Let z = 1+ 2i z = -2-2i, z = 3, 24 =i A. Complex arithmetic (20%) | a. Zi + Z2 b. Z1Zz sle Isles B. Determine the principle value of the argument and graph it (20%) a. 21 b. Z2 c. 23 d. 24
Question 1) Find I = z +2 3z - 2 + 3i 22 + (2i - 2)2 - 4i ] dz, C:\z| = 3, CW a. 4πί b. 8πί C. 2πί d. -2π(3 +i) e. 0.0 f. ο g. -4πί h. 6π
NAME Q1. (30pts) Solve the quadratic equation z2-(3+3i)z +6+2i = 0 by realizing the following plan: (i) find the discriminant A of the equation; (ii) write a program for a scientific calculator to obtain the polar form r(cos 0 + i sin 0) of A and the 'first' root + isin COS 2 of degree two of A; (iii) execute the program, fix the results, find another root A2 of A of degree two (before executing the program, make sure...
Exercise 2 Find logz, Logz and z for (i) -2i; i) z = -1+ i; (i Z (iii z 2/(1 3i) Exercise 2 Find logz, Logz and z for (i) -2i; i) z = -1+ i; (i Z (iii z 2/(1 3i)
please solve step by step to paper NAME: Q1. (30pts) Solve the quadratic equation z2-(9 2i)z +28 12i 0 by realizing the following plan: (i) find the discriminant A of the equation; (ii) write a program for a scientific calculator to obtain the polar form r(cos 0+ i sin 0) of A and the 'first' root + isin 2 of degree two of A; (iii) execute the program, fix the results, find another root A2 of A of degree two...
Find the following: z2+9 e) lim 23į 2-3i z2+i f) lim 2-i 24-1 Write given numbers in the polar form reio: 3 a) (cos 29 + i sin 27)
③ Let 2,= 2-3 , z = 1+ 2i Find (22) 2 0 ③ compute a Ct - ;) e ① & 2 + 1 - ② i + ti
1 2 NAME Q1. (30pts) Solve the quadratic equation z2-(3+3i)z +6+2i = 0 by realizing the following plan: (i) find the discriminant A of the equation; (ii) write a program for a scientific calculator to obtain the polar form r(cos 0 + i sin 0) of A and the 'first' root + isin COS 2 of degree two of A; (iii) execute the program, fix the results, find another root A2 of A of degree two (before executing the program,...
Find zw or — as specified. Leave your answer in polar form. Z = 2 + 2i W= 13-i Find zw.