What is the product of 6+3i and its conjugate
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sqdancefan 3 weeks ago
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Answer:

  45

Step-by-step explanation:

You want the product of 6+3i and its conjugate.

Conjugate

The conjugate of a complex number is created by reversing the sign of the imaginary part.

  (6 +3i)* = 6 -3i

Product of squares

The product of a complex number and its conjugate is recognizable as the factored form of the difference of squares:

  (6 +3i)(6 -3i) = (6)² -(3i)²

Of course, i² = -1, so this becomes ...

  6² -(3i)² = 36 -(-9) = 36 +9 = 45

The product of 6+3i and its conjugate is 45.

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Additional comment

The product of a complex number and its conjugate is the sum of the squares of the magnitudes of the real and imaginary parts. It is always a real number. This fact is used to simplify expressions involving complex numbers.

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