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#