SOLUTION: I am working on expressing negative square roots in terms of j. For example: I have 4* the square root of -8 when i put it in the calculator it comes up 11.313j but the back of

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: I am working on expressing negative square roots in terms of j. For example: I have 4* the square root of -8 when i put it in the calculator it comes up 11.313j but the back of      Log On


   

Question 418197: I am working on expressing negative square roots in terms of j. For example: I have 4* the square root of -8 when i put it in the calculator it comes up 11.313j but the back of the book says 8j* square root of 2. If i put that into the calculator i get the same answer as i was getting before. 11.313j. I don't know how to get the answer in the back of the book.
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
For example: I have 4* the square root of -8 when i put it in the calculator it comes up 11.313j but the back of the book says 8j* square root of 2. If i put that into the calculator i get the same answer as i was getting before. 11.313j. I don't know how to get the answer in the back of the book.
.
The answer in the back of your book is the "exact" answer.
Whereas, the answer you calculated is the approximate "decimal" equivalent.
.
realize that:
sqrt%28-1%29+=+j
.
Thus, your problem:
4%2Asqrt%28-8%29
can be factored as:
4%2Asqrt%28%28-1%29%282%29%282%29%282%29%29
we can extract the -1 under the radical and get:
4j%2Asqrt%28%282%29%282%29%282%29%29
finally, we can pull out a "pair" of the 2's to get:
4%282%29j%2Asqrt%282%29
8j%2Asqrt%282%29