How do you simplify $(7-2i)(2-6i)$ ?

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Answer 1 · 2016-05-17T14:48:11

Multiply the quantities, take the $i^2$ quantity and work with it, and end up with
$2-46i$

There are two parts to working this out: the first is working through the multiplication, and the second is dealing with $i$ .

So let's do the multiplication first:

$7*2=14$
$7*-6i = -42i$
$-2i*2 = -4i$
$-2i*-6i = 12i^2$

Let's now talk about $i$

$i = sqrt(-1)$ , so when we have $i^2$ , we end up with $sqrt(-1)*sqrt(-1) = -1$ . Which means we can take the $12i^2$ term and simplify it to

$12i^2 = 12*-1 = -12$

Now let's combine our new results from the multiplication:

$14-12=2$
$-42i-4i = -46i$

Since we can't do anything further with $i$ and the real term and the imaginary terms can't combine, we are left with a final answer of

$2-46i$

How do you simplify (7-2i)(2-6i)(7-2i)(2-6i)?