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I know that 4*sqrt(-9)-2 simplifies to -2+12i, the problem is that I don't know how to simplify it to that solution. Web2.0 is very helpful, but it needs an option to show a step by step solution! Can somebody explain this so I understand?

OfficialBubbleTanks  Nov 10, 2017
 #1
avatar
+1

Simplify the following:
4 sqrt(-9) - 2

sqrt(-9) = sqrt(-1) sqrt(9) = i sqrt(9):
4 i sqrt(9) - 2

sqrt(9) = sqrt(3^2) = 3:
4 i×3 - 2

4×3 = 12:
12 i - 2

Factor 2 out of 12 i - 2 giving 2 (6 i - 1):
2 (6 i - 1) =-2 + 12i

Guest Nov 10, 2017
 #2
avatar+578 
+2

and yet again, the guests beat every real user to answering my question! thank you!

OfficialBubbleTanks  Nov 10, 2017
 #3
avatar+2190 
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I can explain how to simplify for you! First, let's solely worry about the square root of a negative number first.

 

\(4*\textcolor{blue}{\sqrt{-9}}-2\)  
\(\sqrt{-9}=\sqrt{9}\sqrt{-1}=\sqrt{9}i=3i\) By definition, \(i=\sqrt{-1}\). Here, I broke up the radical into two separate parts.
\(4*\textcolor{blue}{3i}-2\) Operations with imaginary numbers are the same as with a generic variable.
\(12i-2\) Now, rearrange into \(a+bi\) format such that a is the real part and b is the coefficient of the imaginary part.
\(-2+12i\)  
   
TheXSquaredFactor  Nov 10, 2017
 #4
avatar+578 
+2

WOW thank you as well!

OfficialBubbleTanks  Nov 10, 2017

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