The complex numbers z1 and z2 are connected by the relation 1 21 = 22 + -. 22 If the point representing z2 in the Argand diagram describes a circle of radius a and centre at the origin, show that the point representing zi describes the ellipse y? (1+a²)² ™ (1 – a²)² 1 a2

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Q: Let z be a complex variable  z=x+iy question attached in pic

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

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Q: Find the cubic roots of the Complex number Z=-j and graph these roots in the complex Plane? Ans. Wo…

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Q: 1.1 Let z, w e C. Show that |z + w? + |2 - w? = 2(|:|2 + |w?).

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A: Polar form of any complex number z=x+iy z=r cosθ+i sinθ Where r=x2+y2   and    θ=tan-1yx

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Q: Let z, and z2 be two complex roots of the equation z2 + az + b = 0. Assume that the Origin, z1, and…

A: Given  Let z₁ and z₂ be two complex roots of the equation                  z² + az + b = 0. Assume…

Q: Question 2.3b. Let Z1 2 1+i Find the imaginary part of z1 - Z2. C -2 2 3 O -2 2 and 22 = 1; : 3

A: In this question , we will find the imaginary part of z1 - z2 .

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A: Given that: A=1+iB=1-iC=-3+4iD=-3-4i

Q: ow áll the steps) . Write the complex number 2+ iv3 in the form of reit Check the following function…

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Q: If z₁ = 13-101 and 22-15 +91, determine the following: 42₁-522 (Polar Form) COMPLETE THE MISSING THE…

A: We have z1=13-10i , z2=-15+9i Consider: 4z1-5z2=413-10i-5-15+9i=52-40i+75-45i=127-85i Hence,…

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A: We have given α, β, γ, δ are real numbers such that γδ is real number and αδ - βγ ≠0.

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Q: is a reflection 21. Describe the error. z = 2+3i and z, = 2-3i are complex conjugates because z 2 in…

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A: Given that z=3+i convert the given complex number into polar form  also draw the Armand diagram

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A: given a complex number  say w=-10+6j5 now ,  -102+62=100+36                    =136…

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

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Q: From the following rectangular complex number Z-4+3i, Z-2-3i and Z,--5+2i Find the poler form?

A: Given:     z1=4+3i      z2=2-3i      z3=-5+2i For a complex number z, expressed in Cartesian form as…

Q: Find the cube root of Z^3=8i lying in the first quadrant of the complex plane. " i-V3 O 2i+v3 i+2/3…

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Q: Graph the following hegians in the complex plane? | 2-1|=12+1/

A: Given region: We have to graph the given region in the complex plane.

Q: Question 2: (1) (ii) Find the general value of: In(-2+ iw) Plot at least 3 values on the complex…

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