The Conjugate

Multiply the following complex numbers:

Problem: (6 + 3i)(6 - 3i) text annotation indicator

Solution: 45

Problem: (-5 + 4i)(-5 - 4i) text annotation indicator

Solution: 41

Problem: (2 + 7i)(2 - 7i) text annotation indicator

Solution: 53

What do you notice about all of the final products? {They are real numbers, no imaginary parts!}

What do you notice about the two complex numbers being multiplied? {They look similar, but the sign in the middle has changed!}

Complex conjugate of z = a + bi is $LaTeX: \overline{z}=a-bi$ .

Determine the complex conjugate of each of the complex numbers below.

When a complex number is multiplied by its conjugate, the complex part of the number "simplifies out" and we are left with a real number. This fact is helpful when we are dividing complex numbers, watch this video to see how.

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