Good day students on this clip we are gonna how to use the TI calculators to carry out
arithmetic on complex numbers written in rectangular form.
so write down the title.
Using TI calculators on complex number arithmetic we are going to just focus on rectangular
form ok.
Rectangular form the ti-89 does a better job with the polar form than the ti-83s and 84
so lets try the following example.
simplify i to the sixth power if you want to do this by hand you write this as i times
i times i times i times I how many do we have one two three we need one more we use the
fact that i squared equals -1 to pair these up and simplify right so we combine these
two the i ^2 combine these two the i^2 and then combine these two to i^2 and then since
i^2 is -1 because we know that the square root of -1 is i if we square both sides you
get this.
we are going to substitute -1 for all this i so we are going to have umm.
This becomes -1 times -1 times -1 okay so these two multiply to give you positive i
and this is a positive so we end up with positive one times negative final answer is negative
1.
okay so guess what you can do all these calculations with your Ti- eighty TI calculator so how
do you do it?
lets start with the TI-83 first and then I would show you with the other calculator for
the ti-83 all you have to do is find where i is you see this period right here next to
it upper left you have the i there so to access it you have to use the 2ndF button second
period brings up the i raise it to the sixth power enter negative 1 and if you have the
Texas instrument 89 same process but the i is located in a ahh it is located in a different
position os 2ndf (second function) or use catalog should bring up the i and then exponentiation
using the carrot like the other one raised to the sixth power boom negative one ok so
when you are doing higher powers like i^7 this one (the TI83) tends to fall apart so
let us compare them so if I wanted to do i to the seventh for example i to the seventh
is -i (negative i) if i try it right here i to the seventh i get this weird number so
this is basically zero zero minus i which is just negative i but to get a nice clean
result any power greater than six the ti-89 is much more reliable this one requires more
work alright ok so what if we have another example like this.
If we had to do example if we were asked to do something like this 2+i to the third if
I wanted to do this by hand i will have to write this as 2+i times 2+i time 2+i and I
have to foil out the whole thing right the first two if I multiply the first two I get
umm 4, 4 +2i +2i +i^2 and then the last one stays alone.
let us simplify this quantity first before I do the last distribution.
so this becomes 4 plus 4i and then i squared is negative 1 negative 1 and times 2+i and
then combine the four and negative one and you have 3 plus 4 i times 2+i alright so now
we have two complex numbers written in rectangular form so we are going to multiply again foil
it out you going to get 6+3i+8i+4i^2 ok and then we get 6+11i and we know i squared is
negative 1 so it is going to become negative 4 like that combine the 6 and the negative
four and you get two plus 11i okay you see how much work we did how long it is a lot
of room for error but guess what you can do all this calculations computations with your
Ti calculator so all you just do is 2 plus i carrot exponent to the third boom tow plus
eleven i okay so same story with the ti89 basically you have you have ah two plus i
raised to the third power there goes your answer 2+11i alright so I will like you to
use your calculator to try out the following so uh calculator activity calculator activity
simplify number 1 i to the fifth two i to the fourth number 3 2+i times 5 plus i number
4 2+3i to the fifth number 6 1+ i root three to the third and then number 7 is root three
plus 4 i to the fifth power alright so i will like you to try out all these in your calculator
and lets see what you get ok