Pleasantly, when we multiply a complex number z = a + bi by its complex conjugate z, we get a real number which might be called the quadrance or modulus squared of z, namely zz = Q (2) = a² + b2 = \z|². So to simplify a quotient like 1+4i 5-3i' we multiply both numerator and denominator by the complex conjugate of the bottom, namely 5 – 3 i = 5+3*1 Note: enter the complex number a + ib use the Maple syntax a+b*I. This then gives us 1+4i 5-3 i (1+4i)(5–3 i) -734 +i| 2334 (5–3 i)(5–3 i)

Q: What is the basic principle in multiplication of complex numbers?

A: A complex number is a number that can be expressed in the form a+bi, where a and b are real numbers,…

Q: 1. Prove that multiplication of complex numbers is associative.

A: We know that a complex number in the form of a+ib  i.e. z= x+iy =(x,y) where x and y are real…

Q: Find the 5™ roots of the complex number [(2+x) – 5i] , where x = last digit of your ID Number.

A: To find- Find the 5th roots of the complex number 2 + x - 5i, where x = 2

Q: Q2\ If z = 1 + i, what is z3 + z? + z + 1 as a single complex number?

A: Use the following formulae, to simplify the given expression.…

Q: 10 2) z = (-j)()

A: We have to use De Moivre's theorem cosθ+jsinθn=cosnθ+jsinnθ and Eular form of complex number…

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

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

A: Given : 2+3i

Q: Factor over complex numbers into a product of linear factors x2n + x" + 1

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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: If z=3-4i then express these following complex numbers in the form of a+ib: (a) (=+1)(=+i) 2z (b)

A: If z = a + ib and w = c + id then z+w = (a+ib) + (c+id)       = (a+c) + i(b+d)

Q: Lin says, "When you add or multiply two complex numbers, you will always get an answer you can write…

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Q: 4. What is the simplification of the following complex expression (i? = -1) 5-i 3+i

A: To simplify the given complex expression:- 5-i3-i

Q: Is it true that the quotient of two complex number is obtained by dividing their moduli and…

A: Given question says "Is it true that the quotient of two complex number is obtained by dividing…

Q: Present complex number z in algebraic form =* + 23D 35 1-3i

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Q: Express in the form of a complex number a + b i.i / (1 -i)

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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: If a complex number z satisfies z2* = 2-1, what can be said about the number? if the fonrepleziott å…

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Q: 2. It is easier to find the power or the root of a complex number if the numnber is written in form.

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Q: The distance from the origin to the point that corresponds to a complex number is known as the…

A: The absolute value ( modulus ) gives the distance from the origin to that point z , where z…

Q: a

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Q: what is a Complex Conjugates? where the Complex Conjugates came from? how it came in pair?

A: Complex conjugates: If there is a complex number, then its complex conjugate is defined as the…