Sorgan Hemdon
1 answer:
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This one is quite the deal, but we can begin by distributing the negative on the denominator and getting rid of the parenthesis:
See how the denominator now is more a simplification of like terms, with this I mean that you operate the numbers with an "i" together and the ones that do not have an "i" together as well. Namely, the 7 and the -4, the -2i with the -9i.
Therefore having the result:
Now, the
This means that we get the result 7i for the numerator.
In order to rationalize this fraction even further, we have to remember an identity from the previous algebra classes, namely:
The difference of squares allows us to remove the imaginary part of this fraction, leaving us with a real number, hopefully, on the denominator.
See, all I did there was multiply both numerator and denominator with (3+11i) so I could complete the difference of squares.
See how
I'll let you take it from here, all you have to do is simplify it further.
The simplification is quite straightforward, the numerator distributed the 7i. Namely the product
You should know from your classes that i^2 = -1, thefore the numerator simplifies to
You can do it as a curious thing, but simplifying yields the result:
Answer:
Step-by-step explanation:
Well we can simplify the numerator, by multiplying the 4 by the 6 and the m^3 and m^4 (add the exponents, explained in one of my previous answers I think)
This gives us the fraction:
We can now divide the m^7 by m^2 by subtracting the exponents, and the reason why this works, is you're simply cancelling out the m's, If we express this in expanded form we have the following fraction:
Since there is two m's in the denominator and there is also two (more than two) m's in the numerator, we can cancel those two m's out, and we get the fraction:
which can be simplified in exponent form as:
, now all we have to do is divide the 24 by the 3, to get 8
This gives us the answer: