Question

Multiply the following complex numbers. (-3+7i)*(2+5i)

Answer 1

To multiply the complex numbers (-3+7i) and (2+5i), distribute each term in the first by each term in the second, combine like terms, and remember that i^2 = -1 to get the final product -41 - i.

Step-by-step explanation:

To multiply the complex numbers (-3+7i) and (2+5i), we use the distributive property (also known as FOIL in binomials), multiplying each term in the first complex number by each term in the second complex number. The multiplication process is similar to multiplying binomials except we remember that i^2 = -1.

Here's the step-by-step process:

1. Multiply the real parts: (-3) × 2 = -6
2. Multiply the outer terms: (-3) × (5i) = -15i
3. Multiply the inner terms: (7i) × 2 = 14i
4. Multiply the imaginary parts: (7i) × (5i) = 35i^2
5. Remember that i^2 = -1, so 35i^2 becomes -35
6. Add all the terms together: (-6) + (-15i) + (14i) + (-35)
7. Combine like terms: -6 - 35 + (-15i + 14i)
8. The final simplified form is -41 - i

Thus, the product of the complex numbers (-3+7i) and (2+5i) is -41 - i.