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Complex Number Products

Directions: Use the integers -9 to 9, at most one time each, to fill in the boxes twice: once to make a positive real number product and once to make a negative real number product.

Hint

Hint

What has to happen to the imaginary terms to make a complex number a real number?
How can we accomplish that?

Answer

Answer

There are many answers but what has to happen with all of them is that the products of the real and imaginary terms have to eliminate each other.

An example of a negative product is (-6 + 4i)(3 + 2i). This has a product of -18 + -12i + 12i + 8i^2 which is equivalent to -18 + 8i^2 or -26.

An example of a positive product is (6 + 4i)(3 + -2i). This has a product of 18 + -12i + 12i + -8i^2 which is equivalent to 18 + -8i^2 or 26.

Source: Robert Kaplinsky

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