Operations of Complex Numbers

NoGoodAtMath

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I'm at a loss on how to work this problem. (3- square root negative 5) (4 + square root negative 5)
Sorry in advance, I don't know how to type the problem in with square root sign.
 
I'm at a loss on how to work this problem. (3- square root negative 5) (4 + square root negative 5)
Sorry in advance, I don't know how to type the problem in with square root sign.

The square root of a negative number is defined as i times the square root of the positive number, so
\(\displaystyle \sqrt{-5} = i \sqrt{5}\)
where i2 = -1. So we can write your equation as
\(\displaystyle (3-i \sqrt{5})(4+i \sqrt{5})\)

Now just follow the usual rules for multiplication:
(a+b) (c+d) = ac + ad + bc + bd
and simplify and collect terms.
 
I'm at a loss on how to work this problem. (3- square root negative 5) (4 + square root negative 5)
Ouch! They were supposed to have taught you about complex numbers before assigning homework on them! To learn about them, try here. ;)
 
I'm at a loss on how to work this problem. (3- square root negative 5) (4 + square root negative 5)
Sorry in advance, I don't know how to type the problem in with square root sign.
If your problem is given in terms "square root of a negative number", I would NOT give the answer in terms of i.

Presume you know that (a+ b)(c+ d)= a(c+ d)+ b(c+ d)= ac+ ad+ bc+ bd.

Here, a= 3, b= -sqrt(-5), c= 4, and d= sqrt(-5): ab= 3(4)= 12, ad= 3sqrt(-5), bc= -4sqrt(-5), an bd= -(-5)= 5.

So you have 12+ 3 sqrt(-5)- 4sqrt(-5)+ 5

which is the same as (3- isqrt(5))(4+ isqrt(5)) would give you
 
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