+577 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?
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
+577 and yet again, the guests beat every real user to answering my question! thank you!
+2446 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. |
| \(-2+12i\) | |
