SOLUTION: If |z|<0.5, show that|(1+i)z^3+iz|<0.75
Thanks!! :)
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Question 940979: If |z|<0.5, show that|(1+i)z^3+iz|<0.75
Thanks!! :)
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
Note that z^3 + iz| \le |(1+i)z^3| + |iz|)
by the triangle inequality.
Since 
, it follows that 
and 
, and since 
, we have z^3| < \frac{\sqrt{2}}{8})
. Combining,
z^3 + iz| \le |(1+i)z^3| + |iz| < \frac{\sqrt{2}}{8} + 0.5 < \frac{3}{4})
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