+0

# imaginary numbers

+1
318
4
+578

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?

Nov 10, 2017

#1
+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

Nov 10, 2017
#2
+578
+2

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

OfficialBubbleTanks  Nov 10, 2017
#3
+2337
+2

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. $$-2+12i$$
Nov 10, 2017
#4
+578
+2

WOW thank you as well!

Nov 10, 2017