2) The complex conjugate of z is denoted as z. Solve for z in the equation: Z – 12 = j(9 – 27) - giving the answer in the form x + jy, where x and y are real numbers.

Q: (b) Show that i10 is real, even though i or 10i is not.

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Q: Consider the complex number z = (1 – i)(-1-iv3). Find |2| and arg(2).

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Q: Solve, z2 - 4z + 5 = 0 Given that z, = 3 + i, z2 = 4 – 3i, z3 = -1+ 2i and z4 = -2 – 5i, determine…

A: Given equation is, z2-4z+5=0 Now, z=4±16-4×52⇒z=4±-42⇒z=4±2i2=2±i So, the solutions are z=2+i, 2-i

Q: Select one: O a = 1+iv2 and æ = 1 – iv2 O a = -1 - iv/2 and a = -1+i O not in the list O r = -V2 and…

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Q: x2+1 =0 Has soluion in R

A: Solution:

Q: Q4a. Evaluate the complex number e2+3i In(2+i) 3+4i

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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: Find all complex roots of the equation z6+z5+z4+z3+z2+z+1=0.

A: The given equation is z6+z5+z4+z3+z2+z+1=0    .....(1) We know that  z7-1=(z-1)(z6+z5+z4+z3+z2+z+1)…

Q: Express the following complex number in the form x + iy (1 - i)(2 i) (3 - i)

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Q: 12. Consider the quadratic equation az?+bz+c= 0, where a, b and c are real and b2 – 4ac < 0. Suppose…

A: Formula: Quadratic Formula For a quadratic equation ax2+bx+c=0 with a≠0, the roots are given by…

Q: The complex conjugate of z is denoted as z̄. Solve z in equation: z-12=j(9-2z̄) giving the answer…

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Q: Find a - b

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Q: 1. Solve the following equations and list all the roots. a) (x² – 25)(x² + 5x – 14) = 0 b) (2x +…

A: Simplify the equation then find roots.

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: Find all distinct roots (real or complex) of z²+(−5+3i)z+(10–10i). Enter the roots as a comma-…

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Q: Find the real numbers x and y if (x – iy) (3 + 5i) is the conjugate of –6 – 24i.

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Q: The complex numbers z, and z2 are such that z, = -2 + 2i and zz = -2– 2i. Find (a) arg z1 (b) |z21".

A: we have to find the value of the following

Q: 1.4 Describe and sketch the curve in the complex plane given by 2|2| = |2 – 2|. Also write your…

A: We assume z=x+iy then we put this value on the given equation to find the curve and from curve we…

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: 5. Determine all roots of the equation z4 – 9 = 0, and sketch them on the complex plane.

A: Given equation:                            z4-9=0

Q: 3. (Complex Numbers: Quadratic Equations; Scientific Calculators). Solve the quadratic equation 2² +…

A: The given complex equation is z2+(6-3i)z+15-23i=0. (i) To find: Discriminant of the above equation.…

Q: Let z = 3 + 9i and w = 2 – 7i . Find out the following in the x + iy form. 4. z-1 – w-1

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Q: Consider the equation y²Uxx − x²Uyy = 0 a. Discuss the mathematical character of this equation for…

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