Hate to be that guy but I need the extra credit! Reddit complex numbers r/theydidthemath

hate to be that guy but I need the extra credit well I understand so let's take a look we started with 2 is equal to two but we somehow end up with 2 is equal to zero so something must be wrong but what went wrong though well pause the video now think about this first before you watch the solution done okay let's go for this we started with two it's equal to 1 + 1 I agree and then we put this one as Square Ro TK of one I agree okay and then we have one is -1 * 1 yeah right because1 * 1 is of course one and then we'll just go backwards sure and then from here to here we have square < TK of1 times another sare < TK of1 okay and then square root of1 is I likewise this square root of1 is also I I * I is I squ and then I Square by definition we get -1 and finally 1 - 1 will get zero huh spooky right because something must be wrong but where though ready the answer is from here to here it's actually not okay so let me just cross this out but you might be thinking don't we do this kind of things all the time well have a look if we have square root of 4 * 9 can we say that asare < TK 4 * sare < TK 9 well yes because on the left hand side work out the inside first we get square root of 36 and that's equal to work out the square root first here times the square root square root of 36 is 6 2 * 3 is six yes this right here is totally okay and then maybe because we're dealing with negative numbers and also complex numbers so maybe that's the reason but be careful if we have square otk of -1 * 9 can we say that as Square < TK of1 * sare < TK of 9 the answer is yes if you consider the principal value of the square root here's the deal this right here gives a square root of 9 and this right here is I right square root of ne1 I and then square root of 9 is 3 square otk of 9 is indeed equal to 3 I so this right here is 3 I = 3 I checks yeah but here is the deal notice how this and that they are both negative numbers in fact when you have both negative numbers inside and they are multiplying then in that case we are not allowed to to separate the square roots and then multiply so let me write that down right here for you guys if we have a and b being negative numbers then be super careful if you're dealing with square root of a b if you want to say that square root of a Time square root of B in fact this right here is not correct because this kind of things will happen if you decided to do that if a and B are both negative numbers so yeah this is the reason and this is where the mistake is I know I'm late to your response but hopefully you still got your extra credit anyway because I know other people have replied it to this already um R so yeah that's it hold on I just remember that I can give you a question for fun or maybe you can ask your teacher instead so have a look right here let's start with i and of course this is the same as I to the the first Power yeah okay I'm going to write the one as 4 over 4 yeah and then next I'm going to do this this is the same as saying 1 over 4 * 4 right but I'm going to put I to the 4th power first and then times 1/ 4 yeah and then by the rule of exponent we can write this down as I to the 4 raised to the 1/4 yeah and then I to the fourth power is just equal to 1 because again I square is equal to -1 Square both sides I to the fourth power is 1 so this right here we have 1 to the 1/ four power one to any power is just equal to one haa I just showed you that I is equal to one so here is what I can have for you we have all this go ahead and have fun with this

Channel: bprp math basics

Views: 1,131,117

Keywords: complex numbers, bprp math basics, precalculus, square root properties

Id: se0FICK66og

Length: 4min 57sec (297 seconds)

Published: Fri Feb 09 2024