Learn math, science, English SAT & ACT from
highquaility study
videos by expert teachers
Thank you for watching the preview.
To unlock all 5,300 videos, start your free trial.
Introduction to Imaginary Numbers  Problem 1
Carl Horowitz
Carl Horowitz
University of Michigan
Runs his own tutoring company
Carl taught upperlevel math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!
Simplifying a square root using imaginary numbers i. So let’s look at this problem square root of negative 32. So what we really need to do with this is divide it up to its real component, the numbers we know and its imaginary component numbers we don’t name it square roots and negatives.
So we can rewrite this then as the square root of 32 which we know how to deal with, and the square root of 1. Using rules of square roots we know that 16 a perfect square that goes in to 32. So this really we can divide up to into the square root of 16 square root 2 square root 1.
Squarer root 16 is 4 square root 2 we can’t do anything with. And we know that the square root of negative 1 is actually i so we can change this to the number i. So what we really have then is the square root of negative 32 is the same thing as for root 2 i.
Now one thing to be careful of is when we are dealing with square roots it sometimes can be hard to figure out if the 'i' is actually In the square root or not. So if I write square root of 2i not very clearly you don’t know whether that l is in the square root or outside the square root.
So in general what we do is actually put the i before the square root just to make sure that confusion doesn’t occur. So what i would actually write for this answer then is 4i root 2. This answer in theory is perfectly fine but just it could be easily misread not knowing what’s going on, so just put your i outside of the square root to make sure you know what’s going on.
So breaking up a negative square root using real and imaginary components to get the answer.
Please enter your name.
Are you sure you want to delete this comment?
Carl Horowitz
B.S. in Mathematics University of Michigan
He knows how to make difficult math concepts easy for everyone to understand. He speaks at a steady pace and his stepbystep explanations are easy to follow.
Concept (1)
Sample Problems (6)
Need help with a problem?
Watch expert teachers solve similar problems.

Introduction to Imaginary Numbers
Problem 1 5,169 viewsEvaluate:
√32 
Introduction to Imaginary Numbers
Problem 2 4,521 viewsExplaining complex numbers:

Introduction to Imaginary Numbers
Problem 3 665 views 
Introduction to Imaginary Numbers
Problem 4 633 views 
Introduction to Imaginary Numbers
Problem 5 978 views 
Introduction to Imaginary Numbers
Problem 6 581 views
Comments (0)
Please Sign in or Sign up to add your comment.
·
Delete