Question

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

Answer 1

Answer:

26 + 22i

Step-by-step 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:

$26 + 22i$