If a, B, Y, 8 are four complex numbers such that a+ Bt is real and od - By# 0, then z = Y+8t te Rrepresents a (A) circle (C) ellipse (B) parabola (D) straight line

Q: Suppose Zi and Z, are two given complex numbers. Construct graphically a. 3Z1 – 2Z2 b. (1/2)Z, +…

A:

Q: Describe and plot the set of all complex numbers that satisfy the equation Iz - 2il = Im(z) %3D -2

A: We have to plot the complex graph satisfying the given equation.

Q: In an Argand diagram a set of points representing complex numbers z is defined by the equation |z-…

A:

Q: (a) If z is a complex number such that z =8i, write z in the form a +bi. Given that =, =2 b where a…

A: These are complicated & lengthy problems,so I can do it in Advanced mathematics.

Q: Find the sum of the complex numbers in the complex plane. Imaginary axis 10 8 • (3, 8) 6 (-1, 5) 4 2…

A:

Q: Suppose z is a complex number that possesses a fourth root w that is neither real nor pure…

A:

Q: Find the sum of the complex numbers in the complex plane. Imaginary axis 10 8 6 (-2, 3) 4 2 (4, 1) +…

A: To add or subtract two complex numbers, just add or subtract the corresponding real and imaginary…

Q: Ecample 12: Show that the equation of a straight line in the Argand plane can be put in e form zh +…

A: GIven the equation of straight line

Q: 2+7i 3-3i

A:

Q: #1) Find the Midpoint of the line segment joining the points corresponding to 4-3i and 2+2i in…

A:

Q: Plot 6 + 6i in the complex plane. Im 9+ 8 7+ Click to add points 3- 2+ 1 → Re 1 2 3 4 5 6 7 8 9 -9…

A:

Q: If the complex number z = x + iy satisfies the condition |3z – 6i| = 3 , then z lies on Oa. a.…

A:

Q: Let z be a complex number. Then i(cosh(3z) + sinh(3z)) a, ie3z b. ie-3z с. е 3г

A: The given expression is icosh3z+sinh3z where z is a complex number.

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: Plot the complex numbers –4+i and 6–Ni in the complex plane. Imaginary Axis 8- 6-+ 5- Real Axis -8…

A:

Q: Solve over the set of complex numbers. x +32 0 2x2 -10 = -50 17. 18. 19. 3x2 =-12 %3D

A: We have to solve

Q: 2Q Express the complex number 1+ 3i in the form x + yi, where x and y are real numbers. 1-2i

A:

Q: Use DeMoivre’s theorem to find (–√3/2 +i/2)12. Express your answer in complex form.

A:

Q: The conjugate of complex number z satisfy: Oz+z=1 Oz-z=0 Oz-z=2ilmz | Oz+z=2Rez

A: let's consider a complex number , z=Re(z)+i Img(z)  i.e z=x+iy

Q: Q2- The complex number z satisfies the equation 4Z- 32 %3D 2-1 1-181 Then Z = ......... ..*......

A:

Q: Find and graph all the roots in the complex plane. (3 + 14)3

A: We use the approximate value in rectangular form, actual value in polar form

Q: then find (An B C). Z, +Z3 1-i3 Z2 - Z3 (B) right angled isosceles (D) obtuse angled 7. The complex…

A:

Q: Suppose z is a complex number that possesses a fourth root w that is neither real nor pure…

A:

Q: Find all complex numbers satisfying |z + 3 + 4i| = |z − 5|

A: Topic:- complex numbers

Q: The conjugate of complex number z satisfy: z+z=2Rez O Z-N=2ilmz O z+z=10

A:

Q: Find the sum of the complex numbers in the complex plane. Imaginary axis 10 8 (4, 7) 6 4 2 6 8 Real…

A: To find :               The sum of complex number in complex plane.         Adding/Subtracting…

Q: Find the sum of the complex numbers in the complex plane. Imaginary axis 10- (3, 8) (-1, 5) • 4 Real…

A:

Q: Let x₁, x₂ are the roots of the quadratic equation x² + a where a, b are complex numbers and y₁, y2…

A:

Q: 13 Jlgull If z,,z, are two complex numbers then:

A:

Q: Solve for the six sixth roots of z-1 and show their geometric representation on a single complex…

A:

Q: 3. Having two complex numbers z1 & z2, with product z,z2 being real and non-zero, verify if there…

A: Answer is following .

Q: Find and graph all the roots in the complex plane. 3. (3+ (4)

A:

Q: Let z be a complex number such that z, z3 and z5 form an equilateral triangle on the complex plane.…

A:

Q: Let z = 3 – Ai, w = 1+ 2i be complex numbers. For both z and w, what is the: • Real part • Imaginary…

A:

Q: Ecample 12: Show that the equation of a straight line in the Argand plane can be put in e form zb +…

A:

Q: Find and graph all the roots in the complex plane. (3 + i4)5

A:

Q: What is the shape of the graph of the equation z +z = 4 in the complex plane? A vertical line A…

A: In this question, concept of complex number is applied. Complex Number A complex number is denoted…

Q: Suppose z is a complex number (a point in the plane) with angle 30 degrees and radius 2. Suppose w…

A: A complex number having radius r and argument θ is given by z=r cosθ+ι r sinθ. The value of tan θ is…

Q: The complex number z=2eiπ/4 can also be written as z=√2i z=√2+√2i z=2+2i z=√2

A:

Q: Plot the complex numbers -2+i and 7-3i in the complex plane. Imaginary Avis 8. 7- 4 3-+ 2- 1- Real…

A:

Q: To do: 6. If Z1 = 2 + 51, and Z2 = 3 - 21, then what is Z1 x Zz as a single complex number? What do…

A:

Q: 1 (3 + 14)³

A:

Q: Find all points on the complex plane which represent the complex numbers w = (V3- 1)z+1-2i, given by…

A: We know that, z=2eiϕ, ∀ϕ∈ℝ implies the circle of radius 2 with center at origin. Graphically: Now,…

Q: Show that if z1 and z2 are complex numbers then (z1/22) = Zī/22.

A: Given, z1 and z2 are two complex numbers and we have to show,

Q: If the complex number z = x + iy satisfies the condition |z + 1| = 1, then z lies on Circle with…

A:

Q: Find the sum of the complex numbers in the complex plane. Imaginary axis 1아 8- 6 (2, 6) (-1, 5) 4 2…

A:

Q: Find and graph all the roots in the complex plane. (3 + i4)

A: this is a problem of complex analysis.