Which of the following is the conjugate of 6 + 7i?
6 + 7i, 6 - 7i, 7 + 6i, 7 - 6i

Solution:

Non real solutions are a very common occurrence as solutions of polynomial equations.

It should be noted that conjugate solutions always occur in pairs.

Therefore polynomials of degree “n” can have real roots as well as non real roots as solutions.

Complex roots always occur in conjugate pairs.

The conjugate of 6 + 7i is 6 - 7i.

Here “i'' is a representation of √-1.

Hence the solution 6 ± 7i can also be written as 6 ± √-7.

Which of the following is the conjugate of 6 + 7i?
6 + 7i, 6 - 7i, 7 + 6i, 7 - 6i

Summary:

The non real real roots like 6 ± 7i will always occur in pairs. The conjugate of 6 + 7i is 6 - 7i