Math

Things I’ve figured out in math that I want to share so that you’ll have a better understanding or shortcuts to make life easier.

Quadratic equation shortcut if c is 0
Case: ax^2 + bx = 0
Answer: x = 0 or x = -b/a

Imaginary Powers
So the idea is to get to a power of 2 to power of x, and with an even exponent change to 1 and with an odd exponent, stay as -1
Remembering, i^0=1, i^1=i, i^2=-1, i^3=-i
i^623
i^620 * i^3
(i^2)^310 * i^3
Since 310 is even, it must be 1
1 * i^3
1 * -i
Answer: -i

or
i^622
(i^2)^311
Since 311 is odd, it must be -1
Answer: -1

Negative Square Roots + Multiplication (Imaginary Numbers)
I’m going to pose this question to you, what 2 numbers form a negative number? If you thought a negative and a positive number, you are correct. So, with that in mind, the only way to solve a negative square root tells us that there must be 2 solutions.

So solving this you get…
sqrt(-36) = i * sqrt(36) = 6i

Now, while this looks like it has one solution, keeping in mind the rule of a negative and positive, you’ll realize why this next bit isn’t allowed.
sqrt(-18) * sqrt(-2)
sqrt(-18 * -2)
sqrt(36)
Wrong: 6

You can’t multiply two solutions simultaneously which is why you have to break it down into single step processes
sqrt(-18) * sqrt(-2)
i * sqrt(18) * i * sqrt(2)
i^2 * sqrt(36)
i^2 * 6
Answer: -6

 
 
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