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Question
For all complex numbers z1,z2 satisfying |z1|=12 and |z2−3−4i|=5, the maximum values of |z1−z2| is
For all complex numbers z1,z2 satisfying |z1|=12 and |z2−3−4i|=5, the maximum values of |z1−z2| is
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Solution
The correct option is B 2
As per triangle inequality |z1+z2|≥|z1|−|z2|Given |z1=12,|z2−3−4i|=5|z2−3−4i|≥|z2|−|3−4i|⟹10≥|z2|For minimum value |z2|=10So, |z1−z2|=|z1|−|z2|=12−10=2
As per triangle inequality |z1+z2|≥|z1|−|z2|
Given |z1=12,|z2−3−4i|=5
|z2−3−4i|≥|z2|−|3−4i|
⟹10≥|z2|
For minimum value |z2|=10
So, |z1−z2|=|z1|−|z2|=12−10=2
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