Meaning of Multiplying a complex number with its conjugate

We find that the answer is a purely real number - it has no imaginary part. This always happens when a complex number is multiplied by its conjugate - the result is real number. Example. (1 - 3i)(1 + 3i) = 1+3i - 3i - 9i2. = 1+9.

1. When you multiply a complex number by its conjugate?
2. What does multiplying by the conjugate do?
3. Why do you multiply by the complex conjugate?

When you multiply a complex number by its conjugate?

When multiplying a number by its conjugate you should end up with a real number. You can check which 2 complex numbers, multiplied, give you a real number. Let's start with your school's answer. If you do (7-5i)*(-7+5i), you get 49 +70i-25i^2.

What does multiplying by the conjugate do?

If f(x) is a square root function, then multiplication by the conjugate can be used to simplify this expression (in particular, to eliminate the h from the denominator).

Why do you multiply by the complex conjugate?

Complex conjugates are helpful when one needs to simplify expressions such as (3+4i)(−5+6i) ( 3 + 4 i ) ( − 5 + 6 i ) . This is because, when we multiply the numerator and denominator of such an expression by the complex conjugate of the denominator, we get a single complex number.