SOLUTION: Hello I'm new to this site, I wanted to know if there is a easy and short way to solve this problem? (2+3i)(1-5i)

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Question 168737: Hello I'm new to this site, I wanted to know if
there is a easy and short way to solve this problem?
(2+3i)(1-5i)

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

%282%2B3i%29%281-5i%29 Start with the given expression.


Now let's FOIL the expression.


Remember, when you FOIL an expression, you follow this procedure:


%28highlight%282%29%2B3i%29%28highlight%281%29-5i%29 Multiply the First terms:%282%29%2A%281%29=2.


%28highlight%282%29%2B3i%29%281%2Bhighlight%28-5i%29%29 Multiply the Outer terms:%282%29%2A%28-5i%29=-10i.


%282%2Bhighlight%283i%29%29%28highlight%281%29-5i%29 Multiply the Inner terms:%283i%29%2A%281%29=3i.


%282%2Bhighlight%283i%29%29%281%2Bhighlight%28-5i%29%29 Multiply the Last terms:%283%2Ai%29%2A%28-5%2Ai%29=-15i%5E2.


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2-10i%2B3i-15i%5E2 Now collect every term to make a single expression.


2-7i-15i%5E2 Now combine like terms.


2-7i-15%28-1%29 Replace i%5E2 with -1 (note: I'm assuming that you are dealing with imaginary numbers, so remember that i%5E2=-1 )


2-7i%2B15 Multiply


17-7i Combine like terms.


So %282%2B3i%29%281-5i%29 FOILs and simplifies to 17-7i.


In other words, %282%2B3i%29%281-5i%29=17-7i.