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.
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:
[tex]z\cdot \bar z = 2^{2} + 3^{2}[/tex]
[tex]z\cdot \bar z = 13[/tex]
To learn more on complex numbers: https://brainly.com/question/10251853
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