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**+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**+1 **

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

OfficialBubbleTanks
Nov 10, 2017

#3**+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. |

\(-2+12i\) | |

TheXSquaredFactor
Nov 10, 2017