2 Sketch oud describe the set & the Complex numbersthat is govenby 01z-1-i= 2 12 32-3=2

Q: If a complex number z satisfies z = z-1, what can be said about the number? Are con Nay/ Say that…

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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: (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: Let z be any complex number and let Im2| <|2], then which one of the following inequalities is true?…

A: We have to solve given problem:

Q: Let z be a complex number, and w be its additive inverse. Let c be another complex number. If |zc| =…

A: Given z be a complex number and let w be its additive inverse. ⇒z+w=0 and z=w, argz=argw+π Given…

Q: What is the argument of the complex number given by z = (1+ iv3)(1 + i)(cos(0) + isin(0)) Select…

A: We have to find argument.

Q: Re((1+i)z)=1 set an Argand diagram for complex number z

A: Given a complex number : z = x + iy We need to plot for the part : Re((1+i)z) = 1 in the Argand…

Q: Let z be a complex number. Then cot(5z-pi) = cot(5z)?

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Q: Let and z2 be the complex numbers given in the following argand diagram. Find the complex number Z1…

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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: Represent by drawing (Argand) The Complex numbers

A: 8. (a)  The objective is to represent the complex number z=5+2i on the argand plane. Given complex…

Q: (a) The complex numbers w and z are given by w = -1 – j and z = 2+2j. (i) Determine arg(wz). (ii)…

A: Note : According to the company guidelines we can solve only subquestions of first question so…

Q: Pick two complex numbers (like a + bi and c + di) and consider if the following statement is True or…

A: Set of pure imaginary numbers

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

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Q: nced Math For any complex number Z, le|22if Re(Z) 2 1 Re(Z) > 0 Im(Z) > 10 None Im(Z) > 00 answer…

A: Taken z=x+iy and got the inequality on x which is Re(Z)

Q: Let z be a complex number. Then coth(2+m) is equal to * Ocothz O cothz O None of these tanhz, O…

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Q: the complex number z =(2)sqrt2.(e3pi/4) is in eulers form. writing z in the form a+ib. what are the…

A: Given : z = 2√2 ei3π/4

Q: 23. If z is a complex number, show that the sum of z and its conjugate is a real number. ANSWER: z =…

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Q: Represent by dvawing (Argand) the Complex numbers

A: So for better understanding I'm providing hand written solution.

Q: 1. (a) If z1 = -3 - 5i and z2 = -5 – 7i are the two complex numbers, then %3D 21 + 22 + i123 21 – 22…

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Q: Which complex numbers z satisfy z = z? Explain.

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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: Let z be a complex number. Then coth(2+ Ti) is equal to None of these tanhz -tanhz oothz

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Q: Sketch each of the following sets of complex numbers z that satisfy the given equations/inequalities…

A: We will use basic Complex analysis

Q: If a, B, Y, 8 are four complex numbers such that a+ Bt is real and od - By# 0, then z = Y+8t te…

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

Q: If a and b are complex numbers, prove that |a+b|<\a|+\b| .

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Q: Given two complex numbers z and w such that z = (1+ i)w + (3 –- i)w, where w is the conjugate of w.…

A: z and w are two complex numbers. Such that

Q: If u and vare complex numbers such that u = 3 – 5i and v= -6 + i, which of the following is…

A: Given u = 3 - 5i   and   v = -6 + i

Q: 1+i If z = , what is the argument of this complex number? -37 4 -4x 3

A: We have to find argument

Q: If z is a complex number show that the sum of z and its conjugate is a real number Answer: let…

A: Let, complex number z=a+bi Conjugate of the number z ¯=a-bi

Q: Let z be a complex number. Then tanh(2+JTi) is equal to cothz -cothz None of these -tanhz O tanhz O…

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Q: .2 Describe and give the geometric representation of the following point set of complex numbers S=…

A: We shall solve this in next step in details

Q: Let z be a complex number. Then coth(2+ Ti) is equal to -cothz tanhz O -tanhz O None of these

A: I have solved bothe examples for first question first option is correct And for second question last…

Q: Let z1 , Z2 and z3 be the complex numbers given in the following argand diagram. Find the complex…

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Q: Let z, and z, be the complex numbers given in the following argand diagram. Find the complex number…

A: First I am going to find the complex number by using the Euler's identity and then solve the problem…

Q: Let z and w be the complex numbers given in the following argand diagram. Find the distance between…

A: Solution

Q: Give the geometric representation of the following point set of complex numbers: Reli. Rel z). 4.…

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Q: For all complex numbers z1,Z2 then z,+z2> Z2 Select one: O True False

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Q: 5. Which of the following complex numbers is equal to (5 + 12/)- (9 - 6/), for i = V-1 ? -14- 18/ 14…

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Q: Find all complex numbers z satisfying = -i

A: i = -1(i)2 = -1

Q: p and q are complex numbers such that p| = x + 2, |q| -žx – 1, and |p+q] = 2x + 4 %3D On what…

A: I have provided solution in step2

Q: 1. If Iz| = 2, then find the locus of complex number (a + bz), where a, be R.

A: If |z|=2, then find locus of a complex number a+bz

Q: Determine whether the statement "A complex number a + bi can be interpreted geometrically as the…

A: Given: The statement is : "A complex number a + bi can be interpreted geometrically as the point (a,…

Q: Let z be a complex number. Then coth(2+ Ti) is equal to None of these -tanhz tanhz cothz -cothz

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Q: det f be map sending each complex number る→ Show that ((7,7. よ( S()

A: The detailed solution is as follows below :

Q: 3.5. If |2| = 1, then show that az + b 1 bz +a for all complex numbers a and b. ||

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Q: Which statement is false?   All real numbers are complex numbers. All irrational numbers are real…

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Q: b, be complex numbers and N a positive natural number such N¬I i2knx N = απ Τ n = 0 to N - 1 k=0

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Q: Plhet Ziand Zz aretwo complex numbers Such that Z1 = -2+2i, Zz Find arg 3 -2-27

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Q: Find all complex numbers z satisfying 23 = 27 i

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.