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The easiest way to do this is treat i like a variable and multiply the binomials and combine like powers of i, then anywhere there is i², substitute it with (-1).

So (4 + 3x)(3 - 4x) = {using FOIL} 4*3 - 4*4*x + 3*3*x - 3*4*x² = 12 -7x - 12x²

So with x = i, you have 12 - 7i - 12*(i²) = 12 - 7i - -12 = 24 - 7i

One quick check to see if there is an error: The magnitude of the product of the two complex binomials will equal the product of the magnitude of each factor.

Magnitude of a + bi = sqrt(a² + b²). The magnitudes of two numbers that are multiplied are: sqrt(4² + 3²) = 5, and sqrt(3² + (-4)²) = 5. The magnitude of the answer is sqrt(24² + (-7)²) = sqrt(576 + 49) = sqrt(625) = 25, which is 5 times 5.

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14y ago

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Q: The product of the complex numbers 4 3i 3 - 4i?
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