step by step solution thanks alot BurAkEsEN. NAME: Q1. (30pts) Solve the quadratic equation z2(6 3i)z +6-8i 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(cos0+ i sin 0) of A and the 'first' root + isin 2 COS of degree two of A; (iii) execute the program, fix the results, find another root A2 of A of degree two (before...
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...
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)
detailed solution for this one ????? 11. (a) Gi) If w=z+z-' prove that (i) z2 + z 2 = w2 -2 ; 24 +2° + z²+z+1 = z2 (W2 + w+1) = (z? +[1+V5]+1)(22 +[1–V5]+1). (b) Show that the roots of 24 +2+z2+z+1=0 are the four non-real roots of z' =1. (c) Deduce that cos 72° = +(15 – 1) and cos 36° = (15+1).
I. Given Z-2- i and Z2-1 2i. Find the following and express your answer in the form a+ ib (c) Z, Z, (b) 22, +Z, (a).
Find R and angle. Z1 =8+3i, Z2 =2+3i, Z3 =9-((2)^1/2 )i. (vi) z = TEM (vii) 2 = 22 + 231
2iz-1 If f(2) = 27251 2-3i a) Find and simplify f'(z) b) Find f'(1 + i) and write the answer in cartesian form (a + bi).
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...
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 the complex numbers w and z which solve the system of equations (-1+i)w + (-2-3i)z = -12 - 3i (-2+3i)w +(-1+i)z = 0 +10i (Hint: Check your solution by substituting back in)