Question

Find the product and fill in the blanks to write in standard complex number form.

Answer 1

26 + 22i

Explanation:

Given

(2 + 4i)(7 - 3i) ← expand product using FOIL

= 14 - 6i + 28i - 12i² ← i² = - 1

= 14 + 22i + 12

= 26 + 22i ← in standard form

Answer 2

For this case we must simplify the following expression:

`(2 + 4i) (7-3i)`

We apply distributive property considering that:

`+ * - = -\\- * - = +\\2 * 7 + 2 * (- 3i) + (4i) * 7- (4i) (3i) =\\14-6i + 28i-12i ^ 2 =`

We take into account that:

`i ^ 2 = -1`

So:

`14-6i + 28i-12 (-1) =\\14-6i + 28i + 12 =`

Adding similar terms:

`14 + 12 + 28i-6i =\\26 + 22i`

Answer:

`26 + 22i`