Just playing around with the modulus definition doesn't really confirm that thought...
Is it true?
If |z| = |x+iy| < 1, is $$\lim_{n\to \infty} z^n = 0 ?$$
Thanks,
2026-04-03 10:05:01.1775210701
Silly question about complex numbers - if its modulus is < 1, does raising it to higher exponents make it decrease to the real number 0?
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Hint Write $z=re^{i\theta}$ where $|r|<1$. Then $z^n=r^n e^{in\theta}$.
Can you finish?