(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Show that if |z| = 10 then 497 ≤ |z[itex]^{3}[/itex] + 5iz[itex]^{2}[/itex] − 3| ≤ 1503.

3. The attempt at a solution

I'm not an entirely sure how to begin this one, or if what I'm doing is correct.

If I sub in |z| = 10 into the equation; |1000 + 500i - 3| = 997 +500i

Then the modulus of that is sqrt(997[itex]^{2}[/itex]+500[itex]^{2}[/itex]) = 1115.35

497 ≤ 1115.35 ≤ 1503

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# Homework Help: Complex Analysis - Proving an inequality

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