Question

Find the product of these complex numbers. (6 + 8i)(3 - 2i) =

Answer 1

The product of the complex numbers (6 + 8i) and (3 - 2i) is calculated using the distributive property, resulting in a final product of 34 + 12i.

Step-by-step explanation:

To find the product of two complex numbers, (6 + 8i) and (3 - 2i), you use the distributive property (also known as the FOIL method in this context) to multiply each part of the first complex number by each part of the second complex number. Here's the step-by-step solution:

Multiply the real parts: 6 * 3 = 18Multiply the real part of the first by the imaginary part of the second: 6 * (-2i) = -12iMultiply the imaginary part of the first by the real part of the second: 8i * 3 = 24iMultiply the imaginary parts: 8i * (-2i) = -16i2

Remember that i2 = -1, so -16i2 = -16(-1) = 16. Now, combine the results:

Combine the real numbers: 18 + 16 = 34Combine the imaginary numbers: -12i + 24i = 12i

So, the product of (6 + 8i) and (3 - 2i) is 34 + 12i.