I would like to find the solution of this equation, but i do not even know which is the 'leading' term, as in the one with the highest power of t. How would i compare to to atleast find which is the leading term? How could i go about solving this?
I would like to find the solution of this equation, but i do not even know which is the 'leading' term, as in the one with the highest power of t. How would i compare to to atleast find which is the leading term? How could i go about solving this?
It definitely belongs in pre-university, but that's not to say it's not tricky.
First, you need to remember what i stands for; the square root of -1. This is an imaginary number, which means we can't deal with it without going into advanced stuff. You can, however, drastically simplify this problem. Remember that:
Think you can go from here?
I totally disagree with that quote.
Any problem dealing with complex exponentiation is definitely a university level: perhaps number theory or analysis.
Complex exponents do not behave as expected.
For example, if each of is a complex number then .
Only in the case that can we say that
Thus as applied to this problem it can be said that .
Here is a further compilation: where .
It is not clear if t is a complex variable or a real variable.
I assume exp stands for exponential? I must also admit i have never used the arg(t) function.
Perhaps i should clarify this:
This is not a problem i found in a textbook, in fact it is an equation deriving from a function's intersection with the Ox axis.
Background: I solved a differential equation and found the form of a function y(x). As i was curious, i attempted to draw the graph of that function, which was in exponential form and with complex powers. In order to draw the graph, i wanted to see where the function intersected the Oy and Ox axis. In an attempt to find where it intersected the Ox axis, i made it y(x)=0. I worked to try to simplify the equation in order to find the solutions and eventually reached what has been presented as the above equation.
I should note that, in order to simplify and make things clearer for me, i substituted . That is where the t comes from.
With that being said, i expected it not be the average problem. The reason i put it in Pre-University was because it wasn't calculus or differentiation and had nothing to do with those, it was an equation and i did not find a more suitable place to post it. I was an am still curious to how this can be solved for the sheer pleasure of it