For homework help and the general learning experience, try to include the definitions of the terms you are working with. This is beneficial to those helping you, but also the more often you state the definition, the more likely you will remember it for a test or project.
Regarding the "easist...
In English, I believe we more often use the preposition "of." E.g. "Find the multiplicative inverse of to ##x##."
##x^{-1}## represents the multiplicative inverse of ##x##. The phrase ""Find the multiplicative inverse of ##x##" tells us to find ##x^{-1}## . On the other hand, "Find the...
The OP means the multiplicative inverse. The strategy I am explaining yields -m = 1/5. So you have to find the additive inverse at that point to find the multiplicative inverse solution.
EDIT: Since everyone is giving the OP the solution to the problem. The solution process ends with -7 =...
Understanding gcd(n, 12) = 1, might help you limit which numbers are possible solutions. Understanding properties of addition and multiplication in modulo n can provide some tricks to finding the inverse. With the extended Euclidean strategy, (provided gcd is 1) you can set up
##12 = 1 \cdot...
The magnitude is your ##r## value; other names include the modulus and length. The argument is the ##\theta## value; another name for this is the phase.
For problems involving ##A/B## in rectangular form, you do not need to convert to exponential form to solve the problem. All you have to...
Hey @sooyong94,
In your post, I do not understand what you mean by "could have simplified ##(3n-2)^3 +(3n-1)^3 -(3n)^3##. " Could you explain how this simplification method works to confirm the validity of the given equation (Problem Statement)?
If you have memorized summation laws (or have...
Yes, I agree. I was asked how to define a principal root of a complex number. I think I'm just going to persist with my belief that this is just an assumptive framework -- as I really have not seen evidence of notational ambiguity (in my opinion). But thank you.
I am well aware that there is no ordering of the imaginary numbers.
For the real numbers, on the y-axis you do not know whether -1 is geometrically above 0 or below 0. In many math classes, students are conditioned to draw the y-axis with numbers increasing upwards. Yet, there is no reason...
There is no indicators of where to put 1 and -1 on the real y-axis either. The geometry just seems to be part of an assumptive framework to me, much like rotating counterclockwise and locating the cut. You could really do anything.
This seems like a geometric concern - not a notational...
Personally, I would use polar coordinates and cis notation. I see it like a piece of paper that has a tear down the non-postive real-axis (arbitrarily). As you move counterclockwise from the non-positive real axis, you eventually loop over to the backside of the paper. Continuing to rotate...
HOI said it was ambiguous. I am asking for clarification about what makes it ambiguous to HOI or anyone who agrees that it is ambiguous.
I do not agree that ##i = \pm \sqrt{-1}##.
Could you write in greater detail: that is equally confusing. HOI said the notation is ambiguous, and I do not understand if you are also saying the notation is ambiguous. It seems to me you are implying that ##i = \pm \sqrt{-1}##. Further, I do not understand why you would not use ##x^2 =...
In terms of a variety of jobs I have had, I have used number theory more often than calculus. The most helpful topics have been finding solutions to diophantine equations and the concept of check digits. Number theory is particularly helpful for forensic accounting.
In my experience, number...