21. Given that z is a complex number satisfying |2z - 1|=|z2|, prove that |z| = 1 by: (a) letting z = x+iy, (b) squaring the equation and then using the result |z|2= zz.

Q: mplex function f(z) = z(z-21) have a removable

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Q: 2. Let z -1 + i √2 (i) Determine the modulus and the Argument of z. (ii) Locate z, 2², 2³, 24, 25,…

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Q: Q2) Verify v(x.y)-3x3y-y3+5x is harmonic in the entire complex plane then find the conjucte harmonic…

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Q: complex numbers Z1= 4.5-j5.1 , Z2= 3.2- 5.2, Z3= 2.25-j5.6 , Z4= 7.5-j9.2 , then alculate…

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Q: y + 2xy). Find values of a and b so that f (x + iy) will be analytic. Consider the complex-valued…

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Q: Given the complex numbers z, = 2 + j0.51, zz = -0.4- j0.8, and z3 = 3+j3 find; |21Z2 (Z – 23) +…

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Q: Find the conjugate of z = -2 – 4i, and compute zz. z = zz =

A: Given that: z=-2-4i

Q: Let z be a complex number with |z|=17 and let z0=17−11i . What is |z−z0|^2+|z+z0|^2 ?

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Q: (2) Find all the numbers z such that elz = 10i.

A: Consider the given. eiz=10i

Q: The negative complex roots for the quartic equation x* +x² –1=0 are: 1-5 b. i + a. ti 2 c. ti 2 |1+…

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Q: if complex numbers Z1= 4.5-j5.1 , Z2= 3.2- j6.2, Z3= 2.25-j5.6 , Z4= 7.5-j9.2 , then calculate…

A: Given complex numbers are…

Q: 3) The complex conjugate of z is denoted as z. Solve for z in the equation: 27(1 – j2), j 2- j3 1 +…

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Q: 3. (a) Show that, for any complex number z, zz = |z|², z + z = 2Re(z) and Re(z) < |z]. Hence show…

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Q: Find all non - zero complex numbers z satisfying z =i z.

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Q: . Let complex numbers a and 1/a lies on circles (x – xo)² + (y – yo)² = r² and (x- x)² + (y – yo)² =…

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Q: Q1: a) Find the 10th power of 3- 2i using De Moiré's theorem and write the answer in the form a +…

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Q: Find the distance d (in the complex plane) between z = 2 + 7i and w = 11 - 10 i. d = √ (1)² + (9)² X

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Q: Let Z1 and Z2 be roots of the equation z + pz + q = 0, where the coefficients p and q may be complex…

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Q: If z = 1 - 2j and w= 2 - 3j, express 2. w in the form a + bj where a and b are real.

A: Given  z=1−2jw=2−3j

Q: Find the derivatives of the following 1. [sin-(2z – 1)]² 2. cos-1(sin z – cos z)

A: Differentiating complex functions is similar to differentiating the functions with respect to x, but…

Q: B. If the complex function f(z) = u + iv, find u and v for the following complex %3D function: (2 -…

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Q: Given that z, = [3, 0.7], 2₁ = [2,1.2] and z, = [4,-0.5], (c) (i) find a complex number z = [r, 0]…

A: Given that z1=[3,0.7],z2=[2,01.2] and z3=[4,-0.5] To find :  (c) (i)Find a complex number z=[r,θ]…

Q: Let x₁, x₂ are the roots of the quadratic equation v' + a+b=0. where a, & are complex numbers and…

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Q: Determine the cube roots of = (1+j3)(2-j)

A: Given complex number is z=(1+3i)(2-i)                     (1) taking log of both side lnz=(2-i)…

Q: Find the g.c.d. in Z [i] of 2 and 3+ 5i.

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