Complex Numbers on the ACT Multiplication and Division

Remember, a complex number is very similar to a binomial. We’re dealing with imaginary and real numbers at the same time. We already took a look at addition and subtraction, so let’s move on to multiplication and division. These are a little trickier, but only division involves a skill you may not have used yet. Take a look! Multiplication Do you remember having to learn how to FOIL? You multiply the terms of a binomial or complex number in this order: First, Outer, Inner, Last. Let’s take a look at how to do it with a complex number. That leaves us with this: Now remember, , as we already covered. So we get this: Division All right, here’s where things get a little tricky, but stick with me. I promise, we’ll come out on the other side (mostly) unscathed. Let’s say you had to divide 5 + 2i by 6 + 3i. Now, remember, i is just another way of writing √-1. And, according to the ancient laws of math, we can’t have a radical in the denominator (or bottom part) of a fraction. So, it looks like we have to simplify in order to solve this problem. Step One: Conjugate In order to divide complex numbers, what you have to do is multiply by the complex conjugate of the denominator. I heard about half of you get sudden migraines there, but I promise, that’s not as complicated as it sounds. The complex conjugate is just the same exact denominator with one tiny change. Instead of 6 + 3i, we take 6 3i. So our problem now looks like this: Really, all we’re doing is multiplying by a fancy form of 1, so we’re not actually changing the problem; we’re just simplifying it. Step Two: Multiply It looks like we’re out of plastic wrap, which is okay, because all we need is FOIL. Yes, the good old First-Outer-Inner-Last method of multiplying binomials and complex numbers is back again. And this time, it’s personal. Okay, not really. But let’s FOIL anyway. We’ll do the numerator first. That leaves us with this: And now, do the denominator the same way: Step Three: Simplify Here’s our problem so far: We already know that  ,  so let’s change that in both the numerator and the denominator. And now, combine like terms! Watch the magic! Notice how the denominator suddenly doesn’t have any more i in it. We’ve fully simplified this problem! Woo-hoo! Take a nice deep breath, Magooshers! You’ve earned it.

Should Medical Marijuana be Legalized - 275 Words

Should Medical Marijuana be Legalized? (Essay Sample) Content: Name:Course:Instructor:Date:Should medical marijuana be legalized?Even after the US Congress put marijuana under Schedule 1 of the Controlled Substances Act in 1972 on grounds of it not having any acceptable medical use, there have been more than 15 states including DC that have moved bills allowing medicinal purpose only use. The federal law still prohibits the use, sale and possession of marijuana in the US. It is ironical how the same Department of Justice states that it will not challenge the legalization of marijuana despite the fact that it is still categorized together with the likes of Heroin.This calls on the morality and application of common sense. This is because if this federal government can choose to overlook a states allowances on recreational drugs, then the law should be changed to benefit the sick people who need to use this medication without fear of intimidation, and unreasonable searches and seizures which basically goes against the fourth amend ment. According to Forbes, the use of drugs in Portugal went down by half after the decriminalization of all drug use after a decade. The country has since shifted from annually locking up hundreds of thousands of its citizens to curing some few thousand patients addicted. This has also helped in scientific research to understand whole new levels of drug treatment. The idea is not legalization of recreational drug use, but to give allowances in the law for those that need marijuana for their well-being. It is evident that many people are proponents for the legalization of marijuana as indicated by a Siena poll with over eighty percent of New Yorkers showing support for medical marijuana. Lastly, the continued prohibition of marijuana will always require constant distortions of information and selective use of scientific records. This will impact on the credibility of law enforcement organs and scientists. The effects of use of marijuana have been exaggerated over the years forgettin g the fact that, in fact, alcoho...