Question

multiply
$7i(9 - 2i)$
$7i(9 - 2i) = \square$
(simplify your answer. type your answer in the form $a + bi$.)

Explanation:

Step1: Distribute 7i

Using the distributive property (a(b - c) = ab - ac), we have \(7i(9 - 2i)=7i\times9 - 7i\times2i\)

Step2: Simplify each term

For the first term: \(7i\times9 = 63i\)
For the second term: \(7i\times2i = 14i^{2}\), and since \(i^{2}=-1\), this becomes \(14\times(-1)= - 14\)

Step3: Rearrange into \(a + bi\) form

We have \(-14 + 63i\) (rearranging the real and imaginary parts)

Answer:

\(14 + 63i\) (Wait, correction: Wait, step 2 second term: \(7i\times2i = 14i^2=14\times(-1)= - 14\)? No, wait, original distribution: \(7i(9 - 2i)=7i\times9-7i\times2i = 63i-14i^2\). Since \(i^2 = - 1\), then \(-14i^2=-14\times(-1)=14\). So then it's \(14 + 63i\). Yes, that's correct. So the correct steps:

Step1: Distribute 7i

\(7i(9 - 2i)=7i\times9 - 7i\times2i\)

Step2: Simplify terms

\(7i\times9 = 63i\); \(7i\times2i = 14i^{2}\), and \(i^{2}=-1\), so \(14i^{2}=14\times(-1)= - 14\)? No, wait, the term is \(-7i\times2i=-14i^2\). So \(-14i^2=-14\times(-1)=14\). So then combining: \(14 + 63i\).

So the correct answer is \(14 + 63i\).