The complex numbers z1, z2, and z3 are the vertices of a triangle and satisfy the following equation: 21- 22_1-i3 22-%3 2 Therefore, the rectangle is O right-angled isosceles of zero area obtuse-angled isosceles O equilateral

Q: a) i. Given that 'm' and 'n' are powers of 'a', state four laws of indices ii. Explain the concept…

A: Given : m and n are power of a

Q: For the complex numbers • w = 3-5 i • z = -4+7 i Enter exact value of the imaginary part of their…

A: Product of two complex numbers (a+ib)(c+id)=ac-bd+i(ad+bc)

Q: The graph below shows a (nonzero) complex number z on the complex plane. If the constant k…

A: To determine the points that represent the product kz where k is a real number and z is a non-zero…

Q: Find all the complex numbers x that satisfy the equation x5 - ix4 + 5x3-5ix2 + 6x - 6i = 0. Then…

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Q: Find the real and imaginary parts of the complex number.

A: Complex number is a+ib Where 'a' is the real part and 'b' is the imaginary part First we write the…

Q: The complex numbers z1, z2, and z3 are the vertices of a triangle and satisfy the following…

A: Given that z1, z2, and z3 are the vertices of a triangle satisfying the given condition. We have to…

Q: The conjugate of the complex number -4 – 3i is a) 3 – 4i b) 3 + 4i c) -4 – 3i Qd) -4+ 3i

A: A conjugate is where we change the sign in the middle.  i.e        Conjugate of a+ ib = a- ib

Q: Pleasantly, when we multiply a complex number z = a + bi by its complex conjugate z, we get a real…

A: 1+4i5-3i=1+4i5-3i*5+3i5+3i1+4i5-3i=(1+4i)(5+3i)52-(3i)21+4i5-3i=(5+3i+20i+12i2)25-9i21+4i5-3i=5+3i+2…

Q: Completely factor P(x)=x" +2x'+ 8x + 32x- 128 into linear factors, given that - 4i is a zero. P(x) =…

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Q: Two complex numbers z1 and z2 are given by z1 = 3 + 2i and z2 = − 1 − 4i. Evaluate, (a) |z1z2| (b)…

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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: 1-18i Q2- The complex number z satisfies the equation 4Z – 3Z* = 2-i Then Z =

A: complex number

Q: 2 – i Find the conjugate of the complex number in the form of a + bi. 1– 2i

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Q: Find the real and imaginary parts of the complex number. 3

A: We have to find real and imaginary parts of the complex number: 3 We know that if we have complex…

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: 5. Find all the complex cube roots of -8-8i

A: Cube roots of complex numbers

Q: Represent the complex number geometrically.4(-1 + 2i)

A: 4-1+2i

Q: -1 +3i vhat is the real part of the complex number: 7 = 2 A) -1/2 B c) -1 D2V3 2.

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Q: What is the complex conjugate of the root æ 3i? O a = -3i

A: if a+ ib is the complex then its conjugate root is a-ib

Q: what is the product of the complex number 3-4 and 8e53.13i

A: First convert 3-4i to magnitude and angle form then multiply to 2nd one. We get finally 40.

Q: Completely factor over the complex numbers (2x-5) (x+1) = 2

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Q: Find the real and imaginary parts of the complex number. 5 - 7i

A: Known fact:  For a complex number z=x+iy, x is called real part and y is called imaginary part.

Q: Find the value of x in the complex equation (2x - 3yi)(3 + 4i) = 78 - 21i %3D

A: Given complex equation (2x-3yi)(3+4i)=78-21i To determine the value of x  First multiple left hand…

Q: An engineer wants to determine the distance d of the two complex number in the complex coordinate…

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: (b) Find the conjugate and modulus of the following complex number Z = /5+ i6

A: Given complex number is z=5-i6 Since, conjugate of a complex number a+ib is a-ib Hence, conjugate of…

Q: Find the sum of the complex numbers in the complex plane. (4 + i) + (2 + 61)

A: Explanation and solutions is given below....

Q: Let z be a complex number, find therange of real values of a for which the equation. z+alz-1+2i=0has…

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Q: Find the difference of the complex numbers in the complex plane. (4 + 2i) - (5 + 4i)

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Q: z2-4z+6=0

A: The quadratic equation is given as, z2-4z+6=0 Compare this equation with the standard form of…

Q: What is the cartesian form of the complex number: (-1-i√3)4

A: The given complex number: -1-i34.

Q: Represent the complex number geometrically.3 - 5i

A: The complex number 3-5i

Q: Plot the complex numbers -6+i and 1 in the complex plane. `Imaginary Axis 6+ 3+ 1- Real Axis $ -7 -6…

A: We are going to draw

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

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Q: 3i divided by its conjugate? What is the quotient of the complex number 4 品一 Do

A: Topic : division of complex number

Q: 1. Find all complex 4th roots of -8 – 8/3i, plot their location in the complex plane and show that…

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Q: A complex number is graphed as a point on the complex plane below. 2- 1 Real -3 -2 -1 -10 (0, -1)…

A: To determine: The complex number is graphed as a point in the complex plane. Given information: The…

Q: Find the difference of the complex numbers in the complex plane. (3 + 21) – (5 + 3/)

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Q: Find the real part and the imaginary part of the complex number 3 3 V -1+

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Q: 1-18i Q2- The complex number zsatisfies the equation 4Z - 37 2-i Then Z = ......... .........

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Q: Find the sum and the product of the given complex numbers. Plot a quadrilateral with the origin, the…

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Q: Plot the complex numbers -6+i and 1 in the complex plane. Imaginary Axis 5- 3+ Real Axis $ -7 6 -5 4…

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Q: Find the exact solutions to the equations in the complex numbers w2-4w+5=0

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Q: Find all complex solutions of 6x (If there is more than one solution, separate them with commas.)…

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Q: Find the real and imaginary parts of the complex number.

A: Concept  -If a complex number is given as - z = a+biThen,a = real partb = imaginary part

Q: Determine the complex number z that solve the problem 1-18i 4z - 3z %3D 2-i

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Q: Determine the absolute value of the complex number 2 - 3i.

A: Absolute value of complex number z=a+ib is represent by z and  given as z=a2+b2

Roots

The main dissimilarity between real and complex roots is that the real roots are obtained as real numbers, in contrast with the complex roots, which are indicated as imaginary numbers. The standard format for depicting any complex number is in the form of a + bi.