If a +bi and c+ di represent two complex numbers with real components, a, b, c and d, then which of the following represents the imaginary part of their product? (1) ас - bd (3) ab+cd (2) ad – bc (4) bc + ad

Q: (a) How do you add complex numbers?(b) How do you multiply 13  5i2 12  i2 ?(c) Is 13  i2 13  i2…

A: “Since you have posted a question with multiple sub-parts, we will solve first three sub- parts for…

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Q: 3. If a=4-i and b=10+3i, then which of the following is the value of 3a-4b? -28+9i -21-15i…

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Q: a) Determine the moduli and arguments of the complex roots of the following comple (4- j3)-2/5 (b)…

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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: 10. One solution of the equation x³ - 2x2 -2x +4 0 is x = 2. Which of the following describes the…

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Q: Evaluate  3−3i / 1-4i  and express as a simplified complex number.

A: Given,           3-3i1-4i

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Q: Complex arithmetic with conjugates Show that the conjugateof the sum (product, or quotient) of two…

A: Let two complex number are z1= a +i b z2 = c + id

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Q: 1) Melissa and Joe are playing a game with complex numbers. If Melissa has a score of 5 - 4i and Joe…

A: Melissa and Joe are palying a game withcomplex number.Melissa has a score 5-4i and Joe has a score…

Q: 21-5 1. a) Convert the complex number to the form a + bi. 1-3i 1. b) P(x) = x* – 3x' +5x² - 2 What…

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Q: The absolute value |z| = Va² +b² represents the distance of z from 0, and more generally, u – v|…

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Q: M = -4 formulas for the entries of M", where n is a positive integer. (Your formulas should not…

A: Given matrix is: M=24-42 The characteristic equation is: M-λI=024-42-λ1001=02-λ4-42-λ=02-λ2+16=0…

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Q: Write down the complex conjugates of a. 3 +j4 , b. 2 – j

A: Please find attachment for the details solution

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Q: 2. Which of the following statements is NOT true? a. The real part of a complex number, a + bi, is a…

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Q: True or False The square of a complex number issometimes negative

A: Given : The square of a complex number issometimes negative.

Q: (-9 9-10i) (2-7i)

A: Simplification

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Q: 4. The complex cube roots of - 8 -8

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Q: 5. Divide complex numbers. 10 а. 1-2i -3-6i b. 2i

A: Given:                a) 101-2i   Solution:                    Determining the conjugate of the…

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Q: 2. For the complex number 3 + 4i the real part is and the imaginary part is

A: Given  complex number = 3+4i

Q: (a) How do you add complex numbers? (b) How do you multiply (3 + 5i)(2 - i)? (c) Is (3 - i)(3 + i) a…

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

A: We have to find argument

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

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A: topic - complex numbers

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Q: The sum and product of two complex numbers are real if and only if they are conjugate of each other

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Q: 20. Add the complex numbers. (2 + 3i) + (4 – 24) 8 - 6i 6 - 5i 6+i 6+ 5i 6 - i

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Q: 1121 Find the complex conjugate of each number. Find the product of the complex number and its…

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Q: Im working on operations with complex numbers worksheet.  -8(2+7i)+30i 3(5-4i)-(15-7i) 4i/-1+i

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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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A: Let us have two complex numbers  z1=x+iyz2=x'+iy' Now, complex numbers can be written in polar form…