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

A:

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

A: Given : 2+3i

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

A:

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

A:

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: 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: 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…