(a) If C is the circle Izl = R, show that linn (2 + 4)(z2 +22+2) (b) Use the result of (a) to deduce that if Ci is the circle lz-2 5, then (2 +42 +2z+2) Ci (c) Is the result in (b) true if Ci is the circle lz+1l 2? Explain.

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/

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Q: . Define complex variable and complex conjugate with example

A: Topic = Complex number

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

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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: Given the complex number   z=x+yj. Determine z .   Express your final answer in rectangular form

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Q: Let i denote the square root of-1. For the two complex numbers z = 3e and w = 6eT find z, w. Give…

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

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Q: Simplify the complex number a = that a= a + bi. 10 (1+1) ". That is, find values for a, b = R such

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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: 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: Z₁ = (1+i)² 2 (1 - i)² 3 I

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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>z1-z2 (c) z1+z2≤z1+z2 (d)…

Q: If 'a'is a complex number such that z = 1. Find the value of a, so that the equation az? +z+1=0 has…

A: Explanation of the answer is as follows

Q: bers are conjugate. If z, and z2 are two non-zero complex numbers st jal arg (2) ) - arg (z2 ).

A: Since we know that, | Z1 + Z2 | = |Z1| + |Z2| only when the the point Z1 , Z2 and origin are…

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

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

Q: (31 (n, k) > 0. (1) F(x, y, z) = (x - y - 4)i + y + zk (21x² + y² + ² = 1,

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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