(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

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Complex Analysis - Proving an inequality

**Physics Forums | Science Articles, Homework Help, Discussion**