Determine which of the following functions u are harmonic. For each harmonic function, find the conjugate harmonic function v and express u +iv as an analytic function of z. 3.53. (b) 2xy + 3xy2-2y, (a) 3x2y + 2x2-уз-2y2, (d) e_2xy Sin(x2-y2). (c) xe-cosy-yez siny,

Q: Find the 5™ roots of the complex number [(2+x) – 5i] , where x = last digit of your ID Number.

A: To find- Find the 5th roots of the complex number 2 + x - 5i, where x = 2

Q: Q2\ If z = 1 + i, what is z3 + z? + z + 1 as a single complex number?

A: Use the following formulae, to simplify the given expression.…

Q: Sketch the in the Complex Plane curve given by /z-3) - 1z+3i/

A:

Q: Find the root's 51 of Complex equation:

A: Given:      5√(-1)

Q: . Define complex variable and complex conjugate with example

A: Topic = Complex number

Q: Ifz₁, Z2, Z3 are complex numbers such that (2/z₁)=(1/z₂)+(1/z3), then show that the points…

A:

Q: Numerical results should be rounded to two decimal places. Identify the set of complex numbers that…

A:

Q: Draw f (E) in complex numbers system if f (z) = z +Z + izz and E = {z e C:1 < |z| < 3}. %3D

A: Given is a function f(z) and set E. First we let z = x+iy where x and y are real numbers. Then…

Q: Questron No 02:- (a) Reduce the quantity (1-i)(2-i)(3-¿) to real number. (6) let f be the map…

A:

Q: Find the cube root of Z^3=8i lying in the first quadrant of the complex plan

A: Find the cube root of Z^3=8i lying in the first quadrant of the complex plane.  To find the cubic…

Q: (b) Given z is the conjugate of a complex number z such that z=6+8i Find the complex number z whose…

A:

Q: Let z be a complex number. Then Im(-iz+1)= * O =liz-1| O None of these Ozliz-1| Sliz-1|

A: The last option is correct.

Q: Divide. -2i 2+3i Write your answer as a complex number in standard form.

A: The given complex number division -2i2+3i. We have write the number in standard form.

Q: 1. Let z and w be complex numbers. (a) Show that |1+ z w² + |z – w2 = (1+|z|?)(1+ |w/?). (b) Show…

A:

Q: If z=3-4i then express these following complex numbers in the form of a+ib: (a) (=+1)(=+i) 2z (b)

A: If z = a + ib and w = c + id then z+w = (a+ib) + (c+id)       = (a+c) + i(b+d)

Q: Plot the complex number z4 = (√3/2+1/2i)^20 in the Argand diagram.

A:

Q: 4. Evaluate these complex numbers: (a) (40/50° + 20/-30°)¹/2

A: Since you have asked multiple questions, we can solve first question for you. If you want other…

Q: If 4,,2 are two complex numbers then : ollz|-|z||>|z1-z |z,+z2ls\z]\+|z3l |

A: If z1,z2 are two complex numbers, then (a) z1+z2=z1+z2 (b) z1-z2&gt;z1-z2 (c) z1+z2≤z1+z2 (d)…

Q: Find all complex numbers w such that w ² = -1

A: Given that The nth root of the complex number  is

Q: 1. Write the complex number 2+ iv3 in the form of reio . (2 Marks)

A: Here we first find modulus and arg then convert this into polar form

Q: What is the image of the line x = c; c > 0 in the function f(z) = ? ("z" complex number) Z

A:

Q: a

A:

Q: Show that the solution of the equation  4x2 + 24x + 37 = 0 are complex conjugates of each other.

A: Given quadratic equation: 4x2+24x+37=0