Okay i need 2 even Functions and 2 Odd Function and they have to be complex. anyone got one. P.S I have to prove that they are even and odd functions and i having difficulty finding a complex function

Question

anonymous · Answer

Even function f(x) = f(-x)
Odd function f(x) = -f(-x)

And they have to be complex functions also, which means they have to include complex numbers.

We can think about some examples:

(1) Even functions
$$y = i.x^2$$
$$y = i.x^4$$
(2) Odd functions
$$y = i.\sin(x)$$
$$y = i.\tan(x)$$

anonymous · Answer

You can prove them by the above definition.

anonymous · Answer

oh w8 maybe i didnt make the question clear, when i meant my complex i ment by hard lol

anonymous · Answer

im only in grade 12 never learned imaginary numbers

anonymous · Answer

Ok how hard you need :) lol

Is it even function hard enough for you?

$$y = 5x^6 -7x^4 + 100x^2-10$$

anonymous · Answer

yup, do u have another one and i also need 2 odd functions

anonymous · Answer

Ok, just the basic idea is x^2 is even function and sin(x) is odd function examples.

So from 2 basics, I can develop any kind of thinking. The following is an even function, right?

$$y = 0.5\tan(x) - 100\sin(x) + x^3$$

Try to develop more by yourself. I think with 2 basics idea, it is not difficult for you, a 12-grade student.

anonymous · Answer

oh ok thanks

anonymous · Answer

I am sorry, the above answer with tan(x) is odd function (my mistake) :P

anonymous · Answer

alright thanks

anonymous · Answer

wait would y=cos(x) be a even function cuz it symmetrical about the y-axis?

anonymous · Answer

About cos(x). You can easily see that: cos(-x) = cos(x). So cos(x) is an even function. But because it is symmetrical through x-axis, not y-axis