For expressions like:
f(z) = (1+z2)/(1+z4) how does one write the modulus of that in terms of lzl?
i don't really understand the question …
how does one write eg the modulus of 1+z2 on its own in terms of lzl only ??
Well I want to find lf(z)l and show that lzllf(z)l goes to 0 as lzl goes to infinity. So wouldn't I need to write the function above in terms of lzl, multiply by lzl, and show that it goes to zero?
in that case, write z = reiθ
hmm yes okay. So in that case i would for instance get:
(1+lzl2ei2θ)/(1+lzl4ei4θ). But still that doesnt really give me the modulus for the whole expression?
ok, so multiply by |z| and then let |z| -> ∞ …
what difference do the θ terms make?
(btw, we normally write 2iθ rather that i2θ)
oh well but the expression above is f(z) not lf(z)l = mod(f(z)), and I wanted to show that lzllf(z)l -> 0 as lzl->∞..
Edit: Oh well if f(z) goes to zero then surely lf(z)l does too.. So nevermind, unless you can have lf(z)l->0 even though f(z) doesn't? Nah that wouldn't make sense right..?
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