Determine whether the statement is true or false. Justify your answer. a. The modulus of a complex number can be real or imaginary. b. The distance between two points in the complex plane is always real. c. The modulus of the sum of two complex numbers is equal to the sum of their moduli.

Q: 1. Having the following complex numbers A= 5 – 21 and B= 3 + 8i a) A + B b) В — А c) A*B d) What is…

A: a) Given complex numbers A=5-2iB=3+8i In addition of complex numbers real terms are added and…

Q: The complex number u = a + bi is an ________ ________ of the complex number z when z = un = (a +…

A: Consider "The complex number u = a + bi is an ________ ________ of the complex number z when z = un=…

Q: The absolute value, or __________, of a complex number a + bi is the distance fromthe ______ to the…

A: Given:   The absolute value, or __________, of a complex number a + bi is the distance fromthe…

Q: YOve the equaHIon: X4+3x^ta=0 WITR answers hs a ist of complex number. %3D

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Q: Let a = 1+bi be a complex number, b>0, such that a is a real number. Evaluate 1+a+a² + . + a". ....

A: Given a complex number : a=1+bi where b>0 It is given that  a3 is a real number. We need to find…

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: 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: Express the complex number in exponential form z=rei*theta *-2pi(i) *2/(1+i)

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Q: roitulos woy olit bas vllnaitvinua valienpsol ) Simply the complex number and write in a + bi form…

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Q: Simplify the complex number z=j(-1+j). Then, find the modulus of the complex number z and the…

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Q: (b) Find the conjugate, argument and modulus of the complex number Z =1+i3

A: Recall: If z= x+iy , then (i) Modulus of z , z=x2+y2(ii)Conjugate of z is z¯ =x-iy(iii) Argument =…

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

A: To find cube root of given complex number first convert into euler form then take cube root. Then…

Q: Let z be a complex number. Then cos(3z)-i is unbounded in C. * False O True

A: From Liovilles thm we can say Every non constant entire function is unbounded.

Q: Use De Moivre's theorem to change the given complex number to the form a + bi, where a and b are…

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Q: 29. When z = z If z and z are equal, what can you say about the location of the point z in the…

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Q: Graph the complex number, find its modulus and put the complex number in polar form with arguement Θ…

A: -1 - sqrt(3)/3 i = -1 - 0.577i (approx) This is similar as (-1,-0.577). Plotted it on graph.

Q: Justify your answer. Say if its true or false 1.- If z1, z2 and z3 are complex numbers such that…

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Q: i) ii) (AB) = B*A', ii)AA)* = TA', (A+B)* = A* + B', %3D %3D %3D where A is a complex number and At…

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Q: Use De Moivre's theorem to change the given complex number to the form a + bi, where a and b are…

A: We need to write (1-√3i)12 in the form a+ib

Q: A complex figure is any figure that has 5 or more sides. O True O False

A: We have to evaluate the statement, ''A complex figure is any figure that has 5 or more sides.'' is…

Q: (A) Simplify the complex number z and express it both in rectangular and polar form. (3 + j6)(6+ j4)…

A: It can be calculated as given below:_

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: tind all the roots the complex nunbers given a) z² =-32 b) z?+ (i-2)z +(3-1) = 0 %3D %3D

A: In the given question we have to find the root of the equations (a). z5 =-32(b).…

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

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Which complex number labeled in the complex plane below is the plot of the complex number 1+2i? imag…

A: Complex number

Q: The ________ ________ of the complex number a + bi is the distance between the origin and (a, b)

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Q: Identify the real part, imaginary part and magnitude of the complex number ecos(theta)+jsin(theta)

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Q: z is a complex number with |2| = 6. The triangle formed by z, z?, z° has a right %3D angle at z.…

A: Use the following formulae, to obtain the solution. i2=-1 x+iy=x2+y2 If z=x+iy is a complex number,…

Q: Graph the complex number, find its modulus and put the complex number in polar form with arguement Θ…

A: Graph the given complex numbers as shown below.

Q: Determine u = cis(pi/16) v = cis(5pi/16) are two of the nth roots of some complex number z.what is…

A: Given: Determine u = cis(pi/16) v = cis(5pi/16) are two of the nth roots of some complex number…

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: Simplify the complex number z = j(-1+ j) and plot the result on your Argand diagram. Then, find the…

A: Given :           z = j(-1 + j)        To simplify z and to plot the result on Argand diagram.…

Q: Show the 2 points that satisfy the equation in the complex pione. i) | 2 - 11 = 2.12 +1|

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Q: Find all complex numbers which make the following equations true |z+ 1| = and 2 + 1| = 1

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Q: Solve the following inequality in the complex variable z: Re ((z − 1)(z − 2i)) ≥ Re(z − 1) · Re(z −…

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Q: Use De Moivre's theorem to change the given complex number to the form a + bi, where a and b are…

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Q: 1. Write the complex number i+= in the form of rele V3

A: The polar form of complex number  is    , where     and  and .

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

A: Given point set of complex numbers is S=z∈ℂ : 1<Re2+iz+1≤3

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

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Q: Let a be a complex number 0. What is the absolute value of a/ā? O (A) 1. (B) 2. (C) 3. 4. O 000

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Q: A complex figure is any figure whose angles are not all congruent. True O False

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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: 4. (a) What is the complex plane? How do we graph a complex number z = a + bi in the complex plane?…

A: (a) Complex plane: The complex plane is defined as a Z-plane which is established by real axis and…

Q: 1. Which of the following does NOT describe the modulus of the complex number a + bi? a. The length…

A: 1) a) since |a+ib| describe √(a^2+b^2) implies distance from origin to coordinate (a, b).      b)…

Q: What are all the cube roots of -1 in the complex plane? Mutiple choice options: 1 -1 e(5π / 3 i)…

A: Given problem:- What are all the cube roots of -1 in the complex plane?   Mutiple choice options:…

Q: Which of the following provides the rectangular form of a complex number? A z=a+ bi B z=r (cos theta…

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