It is true that the product of a complex number and its conjugate is a real number and this can be determined by using arithmetic operations.
Let the complex number be (a + bi). Therefore, its conjugate is given by (a - bi).
The following calculation can be used to determine the product of a complex number and its conjugate:
= (a + bi).(a - bi)
Multiply (a) by (a - bi) and then multiply (bi) by (a - bi) in the above expression.
[tex]\rm =a^2-abi+abi-b^2i^2[/tex]
Simplify the above expression.
[tex]\rm =a^2-b^2i^2[/tex]
Remember the value of ([tex]\rm i^2 = -1[/tex]). So substitute the value of [tex]\rm i^2[/tex] in the above expression.
[tex]\rm = a^2+b^2[/tex]
From the above calculation, it can be concluded that it is true that the product of a complex number and its conjugate is a real number.
For more information, refer to the link given below:
https://brainly.com/question/9876116
