Two Inequalities Involving Complex Numbers
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I have two problems with complex numbers:
1) Use properties of moduli to sow that when |z3| does not equal |z4|,
Re(z1 + z2) / |z3 + z4| <= (is smaller or equals) (|z1| + |z2|) / (| |z3| -|z4| |)
2) Verify that sqrt(2) * |z| >= |Re z| + |Im z|
(suggestion: reduce this inequality to (|x| - |y|)^2 +. 0
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Solution Summary
We prove two inequalities involving complex numbers.
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1) We have
Re(z1 + z2) <= |z1 + z2| <= |z1| + |z2|
and
|z3 + z4| >= ||z3| - |z4||,
whence ...
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