Sunday, May 31, 2020
Imaginary Numbers on the ACT
Sadly, ACT imaginary numbers arenÃ¢â¬â¢t the ones you may have come up with as a child, like eleventy-twelve. (Though if any of you become mathematicians one day, please make that happen. It would be fun!) No, real-life imaginary numbers (and isnÃ¢â¬â¢t that a weird turn of phrase) were discovered/invented as a way to take the square root of a negative number. With real numbers, we canÃ¢â¬â¢t do that, but by using our imaginary number, we totally can! Basically, if you take the square root of -1, you wind up with the imaginary number i Translated into math, it looks like this: Simple so far, yeah? Good, because weÃ¢â¬â¢re about to introduce a little complexity up in here. Simplifying Imaginary Numbers on ACT Math Okay, letÃ¢â¬â¢s take a look at an example. Say you needed to find the square root of -16. Well, how do you get the number -16? One way is to multiply 16 and -1, right? So letÃ¢â¬â¢s rewrite it like this: We already know that Ã¢ËÅ¡-1 is i, and you should know that Ã¢ËÅ¡16 is th cycle, and everything before that cancels out. i^53 = i and i^54 = -1, so the remaining sum is i-1, so our answer is D. Remember Ã¢â¬Å"I -Won, -I Won,Ã¢â¬ and its easy! For more on imaginary numbers, check out Kristins explanation below!