Question

Explain and demonstrate the multiplication of complex conjugates using 2+3i and its complex conjugate. Be sure to discuss all steps of the process, including the solution and to which number set it belongs.

Answer 1

The product of a complex number and its conjugate is (a + i b) · (a - i b), where a and b are real numbers, and the result for the complex number 2 + i 3 is 13.

What is the multiplication of a complex number and its conjugate

Let be a complex number a + i b, whose conjugate is a - i b. Where a and b are real numbers. The product of these two numbers is:

(a + i b) · (a - i b)

Then, we proceed to obtain the result by some algebraic handling:

a · (a + i b) + (- i b) · (a + i b)

a² + i a · b - i a · b - i² b²

a² - i² b²

a² + b²

If we know that a = 2 and b = 3, then the product of the complex number and its conjugate is:

$z\cdot \bar z = 2^{2} + 3^{2}$

$z\cdot \bar z = 13$

To learn more on complex numbers: brainly.com/question/10251853

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