Determine whether the given expression is a binary operation or not. Explain your answer through narration and/or computation. Multiplication on the complex numbers (C) Subtraction on prime numbers (P) Multiplication on integers (Z)

Q: So to simplify a quotient like we multiply both numerator and denominator by the complex conjugate…

A: The complex number,      1+4i5-3i

Q: In multiplying two complex numbers, what should be done in order not to go through the long process?…

A: The general form of a complex number z=a+bi in modulus argument form is z=r cosθ+isinθ where r is…

Q: (7) The line from the origin to a complex number makes a cer- tain angle with the horizontal axis.…

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Q: form Z=6cis135 degrees

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Q: Express 8/-121 as a complex number (in terms of i): 8-121 = %3D

A: The expression is given as , -8-121 Express as a complex number.

Q: What is the additive inverse of the complex number 3-7?

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Q: Give a specific example of a complex number z where Arg(z) ≠ −Arg(z). Write your answer in…

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Q: Explain and demonstrate the multiplication of complex conjugates using 2 + 3and its complex…

A: Given : 2+3i

Q: (6-7)- (20 + i) + (-16 + 13) 8.

A: We are asked to subtract or add  the given

Q: 8- 815 Simplify the expression by using complex 6 + 2i /5 conjugates to write quotients of complex…

A: The given expression is 8-8i56+2i5To simplify it

Q: Use DeMoivre's Theorem to find the indicated power of the complex number. Write the answer in…

A: Given; [5(cos 80°+ isin80°)]3

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: 1. Write the complex number i+ 2 in the form of reio

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Q: Represent the complex number geometrically.-2 - 6i

A: Complex numbers are defined as numbers in the form z=a+bi where ii is the imaginary part and a and b…

Q: Do complex numbers have inverses under the complex additionoperation (‘additive inverses’)? Explain.

A: z = a+ib is a complex number Then additive inverse of z is = -a-ib

Q: Combine the complex numbers. (8– 71)-(2- 41)

A: A complex number will have a Real part and an Imaginary part. While combining  two complex numbers,…

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

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Q: Write the expression complex number in standard form. as a 1) (-8 + 8i) – (2 + 4i) 2) (8i) + (-4 -…

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Q: In Exercises 77-80, determine whether each statement is true or false. If the statement is false,…

A: Statements are given , we have to check whether it is true or false

Q: 13. Find the complex number.

A: Given real part=4 Imaginary part=-7i

Q: (b) Write the complex number (-+03 in the simplest form

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Q: Determine whether the given sets are binary operations under addition, subtraction, multiplication,…

A: Given that: A set of complex number.

Q: Represent the complex number geometrically.-(3 - 6i)

A: Represent the complex number geometrically.-(3 - 6i)=-3+6i

Q: 2.2 Simplify the complex power ()-“ and leave your answer in its simplest form.

A: Given 1+i1-i-2i

Q: Write the expression as a complex number in standard form. I) (-8 + 8i) – (2 + 4i) 2) (8i) + (-4 -…

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Q: 7. (13+ 11i) - (-19)

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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: 1. Write the complex number i+2 in the form of reio

A: The complex number z can be written in the form of . The value of r can be obtained from the formula…

Q: Write the complex number in standard form. (2-J-15)* O -11+ /15i O 4- 15/5i O-11-4/15i O -11+4/15i…

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Q: Add or subtract the complex numbers. 5. (18 + 21) + (-3 - 18i)

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Q: 2. Divide the complex numbers. 7+ 31 7- 3i 20 + 214 20. 21 29 29 1-i 29 – 29i O1+i

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Q: Simplify the complex number: (-√5,10)/(√10  , 5)

A: A complex number is written in the form of a+ib, where a and b are real numbers, and 'i' is called…

Q: Determine whether the statement "When I add or subtract complex numbers, I am basically combining…

A: Consider two complex numbers a+bi and c+di where a,b,c,d are real numbers   Add both complex numbers…

Q: (8) Add and multiply the following pairs of complex numbers. (a) 1+21 & 3+ i (b) 3-21& 4 + (c) 5-61…

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Q: So to simplify a quotient like we multiply both numerator and denominator by the complex conjugate…

A: We can solve the given problem as follows:

Q: 13 (b) Write the complex number (-+0 * in the simplest form

A: here we will find simplest form of complex no.

Q: a. Find the modulus and argument of the complex number here, x = last digit of your ID number.

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

A: The complex number 3-5i

Q: With addition and multiplication as in definition of complex numbers, prove that the right…

A: According to the question, Let C represents the set of all ordered pairs a,b of real numbers a and…

Q: Identify the complex conjugate of the complex number. 55. 9-i 56. -2i Choices for 55-62: 57. -4-5i…

A: For complex numbers ,we find the complex conjugate by changing the sign of the imaginary part of the…

Q: Write the complex conjugate of the complex number. Then multiply the number by its complex…

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Q: 13. Give a justification for the statement If a is a complex number then there is another complex…

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Q: (1+ i)18 Za (1 – iv3)9

A: Given: za=1+i181-i39 We know that cosθ+isinθ=eiθ…

Q: What is the first step in writing the complex number -1 + i in trigonomet-ric form?

A: Consider z=x+iy is any complex number, so polar form is, z=x+iy=rcosθ+isinθWherer=x2+y2θ=π-tan-1yx…