1. Find the following products of complex numbers a. (2 + 3i)(4 – 2i) c. (-1 – 2i)(2 + i) b. (2 – i)(-2 – 3i)

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: (a) 2122 + 22Z3 + 2321 (b) (c) Re(z) +Im(2?

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

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: 8. Consider the complex number z = 5+8i and w = 3– 3i. Write down the real and imaginary parts of…

A: Proceed as shown

Q: Given the two complex numbers: 2₁ = 2 + 4i and Z₂ = √5 -3i 1) Find the value of the complex number…

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Q: Plot the complex number. 3 + V3i Imaginary Imaginary axis axis 4| 4| 2 2 Real Real -4 -2 4 axis -4…

A: To plot the given complex number

Q: For the given complex numbers: Z1 = 4 - 2i and Z2 = -1 +3i, find: Z1 - 2 22 Select one: a. 6 - 8i b.…

A: Given thatZ1=4-2iZ2=-1+3i2Z2=-2+6i

Q: Divide the following complex numbers and express the result in standard form, a + b i, where a and b…

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Q: Among the complex numbers below, which is not a result of one of the following calculations: -1+ 2i…

A: We have to check

Q: Divide the following complex numbers and express the result in standard​ form, a+bi​, where a and b…

A: We have to divide the following complex numbers and express the result in standard​ form.

Q: Q4a. Evaluate the complex number e2+3i In(2+i) 3+4i

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Q: For the complex numbers w = 7 + -6 i • z = 4 - 5 i Enter the absolute value of 2w 3z in the space…

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Q: iv) in complex number z3. (7)? = |z|?. z

A: Complex number: A complex number has the form z=x+ιy, where x is called the real part and y is the…

Q: 3. How may the following complex numbers be obtained from z = x + iy geometrically? Sketch. а. 2 b.…

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Q: The remainder of this question concerns the complex numbers z1 = 2 + j4 and z2 = −3 + j4 (a)…

A: To find Z1+Z2

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

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Q: The complex number Z1and Zzare given by, Z1 = 3 – 5i and Z, = -1+4i Determine: 221 + 5Z2 O1+ 10i 01-…

A: Given: Z1=3-5i & Z2=-1+4i We know that; a+bi±c+di=a±c+b±di And ca+bi=ca+cbi, where c is scalar.

Q: O Find all the complex roots of (-1 – 7i)/' 1/7

A: As per our guidelines, we are supposed to solve only first question.

Q: 6. Find the following complex numbers in the form r+ iy, whe and y are real. (i) (3+7i) + (6 – 10i)…

A: we have to find complex numbers in the form of x + i y  Adding real part with real part and…

Q: 3. Determine all complex numbers z for which |2z – 1| < 2|2 – i|.

A: The given problem is to find all the complex numbers that satisfies the given complex inequality.

Q: 4. What is the rectangular form of the complex number 7.2e(7a/13)i? c. 7.15 – 0.87i a. -0.87 + 7.15i…

A: Note: As per bartleby guidelines for more than one questions asked, only one question is to be…

Q: 4. Perform the following operations involving complex numbers: a. (2 + 7i) + (3 – 4i) b. (9 + 5i) -…

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Q: 8. Consider the complex number z = 2 + i and w = 7 – 2i. Write down the real and imaginary parts of…

A: Given : The complex numbers z = 2 + i  and w  = 7 - 2i.   To write the real and imaginary parts of…

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: Perform the following operations on the complex numbers. a) (4– 6i) – (-8 - 9i) b) (4 – 6i)(-8 – 9i)…

A: (a) Perform the subtraction operation for the given complex numbers.…

Q: What is the algebraic form of the complex number 13 e 12+5i 5-12i 12-5i 5+12i

A: We will use the basic theory of complex numbers to answer this question.

Q: Solve the following complex numbers: Z1 = 5+3i; Z2 = 4+5i ; Z3 = 3-i 1. The product of Z1*Z2 2. The…

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Q: The remainder of this question concerns the complex numbers z1 = 2 + j4 and z2 = −3 + j4 (a)…

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Q: 3. How may the following complex numbers be obtained from z = x + iy geometrically? Sketch. b. (-z)…

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Q: Find the distance between the pair of complex numbers. (7 - 2i) and (5 + 8i) O4/26 V194 O2/2 2/26

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Q: 4. Preform the following operations and express the answer as a complex numbers. а) (15 — 20) — (6 +…

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Q: Given the complex numbers z = 2 + j3,zy = -1 - j2, and z3 = 4 + j4 find; Z₁ Z122 Im…

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Q: 1. Find each of the following products of complex conjugates. Express your answers in simplest form.…

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Q: Z = (1 - j)¹-2j

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Q: Represent the following complex numbers in polar form: 6. -i 7. -4 8. 2+2/3i 9. -5+ 5i 10. 2 – 2i…

A: 6. It is given that the complex number -i, Note that: The complex number a+ib  can be written in…

Q: For the given complex numbers: Zı = 4 - 2i and Z2 =-1 +3i, find: 2*Zı - Z2 Select one: a. 5- 5i O…

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Q: (b) Calculate (i) z1 + Z2. (ii) z, Z2. (iii) z1/z2.

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Q: For the given complex numbers: Z1 = 4 - 2i and Z2 = -1 +3i, find: Z1 - 2*Z2 Select one: O a. 5- 5i…

A: Given complex numbers are Z1=4-2ι and Z2=-1+3ι. We have  to calculate Z1-2Z2. We know that a complex…

Q: 2. Write the given complex numbers in the form a + bi. 3 (a) 를 + 을-2유 (b) 2,0 + + 5i 5- 12i (c) 2-4i…

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Q: Ifz is a complex number, then sin-z can be written as (A)-i In iz+ (1-z) (B)t In [iz + (1 -z)]…

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Q: Q(1): Derive formula for the product and division of two complex number.

A: Our objective is to derive formula for product and division of two complex numbers...

Q: 1. Evaluate the principal value of the complex number : (3 + j4)(3+j4) O A. 3 + jo.592 О в.3-ј0.592…

A: Given: The complex number, 3+j43+j4   To evaluate: The principal value of the given complex number

Q: Express the complex number equation below into exponential form. 2i (3 + i) (1 + iv3) = -8 2e# )…

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Q: (a) The complex conjugate of 3 + 4i is 3 + 4i (b) (3 + 4i)(3 + 4i)

A: (a) For a complex number a+ib,  a+ib=a-ib So  3+4i=3-4i

Q: 3.1. Express each of the following complex numbers in the form x+iy: (a). (V2 – i) – i(1 – v2i),…

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Q: 1. Given two complex numbers z, = 2+i and zz =1-2i. a) Determine the value of k if -= kz, b) Express…

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Q: Let z2 = -V2 + i/3, w = -3+ 3i and p= -3– 2i. 1. Find all the complex numbers given by In z2.

A: It is given that