Question #eae0d

1 Answer
Oct 26, 2017

28-35i is the correct result.

Explanation:

The answer is indeed 28-35i. Here's how:

Take the original problem and use the distributive property to multiply out the product:

-7i(5+4i) = (-7i)(5) + (-7i)(4i)

Now, multiply the individual products out:

(-7i)(5) + (-7i)(4i) = -35i - 28i^2

Next, recall from the definition of the imaginary unit i that the quantity i^2 = -1 and substitute this:

-35i - 28i^2 = -35i - 28(-1) = -35i + 28

Lastly, per standard form/convention, we always write a complex number with the real portion first, and the complex portion second. Thus:

underbrace( -35i )_ "Complex" + underbrace( 28 )_ "Real" = 28 - 35i