Question

What is the product of complex conjugates? (1 point)

Answer 1

Answer:

A. the product of complex conjugates is a difference of two squares and is always a real number

Step-by-step explanation:

Given a complex number z1 = x+iy where x is the real part and y is the imaginary part.

The conjugate of a complex number is the negative form of the complex number z1 above i.e z2= x-iy (The conjugate is gotten by mere changing of the plus sign in between the terms to a minus sign.

Taking the product of the complex number and its conjugate will give;

z1z2 = (x+iy)(x-iy)

z1z2 = x(x) - ixy + ixy - i²y²

z1z2 = x² - i²y²

.since i² = -1

z1z2 = x²-(-1)y²

z1z2 = x²+y²

The product gave a real function x²+y² since there is no presence of complex number 'i'

It can also be seen that the product of the complex numbers z1z2 is like taking the difference of two square. An example of difference of two square is that of two values a and b which is (a+b)(a-b).

From the above solution, it can be concluded that the product of complex conjugates is a difference of two squares and is always a real number.