Video:How to Solve i Functions in Equationswith Bassem Saad
Solving functions with imaginary numbers, or i, is an important part of calculus. Learn how to solve i functions in equations in this how-to video from About.com.See Transcript
Transcript:How to Solve i Functions in Equations
Hi, my name is Bassem Saad. I'm a Math Ph.D. candidate at U.C. Davis, and I'm here today for About.com to show you how to solve functions involving i.
Solving Functions Using I
Remember, i squared equals negative one; or, equivalently, negative i times i equals one. Allowing this imaginary number to exist gives solutions to old problems. For example, say we had x squared plus one equals zero. We can solve for x by subtracting one from both sides to give us x squared equals negative one. Then we take the square root to give us plus/minus the square root of negative one; but the square root of negative one is just i. So now we have our solution to this polynomial.
Using I as a Coefficient
i can also come up as a coefficient in an equation. We can use the properties of i to still find solutions to the equation. For example: i times x minus five equals one. We can still solve for x. First thing we want to do is get everything that's not times x to one side of the equation. So we can add five to both sides to get i times x equals six. The next thing we want to do is get rid of this i. But, remember, negative i times i equals one. So if we multiply negative i times both sides – so negative i, times negative i – we get our solution, which is just x equals negative six i.
Every electrical engineer must be able to solve equations involving i. This skill is crucial for physicists, engineers, and scientists of all types.
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