Question

Question #eae0d

Answer 1

`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`