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Question
For all complex numbers Z1,Z2 satisfying |Z1| = 12 and | Z2−3−4i| = 5 , the minimum value of |Z1−Z2 | is
For all complex numbers Z1,Z2 satisfying |Z1| = 12 and | Z2−3−4i| = 5 , the minimum value of |Z1−Z2 | is
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Solution
The correct option is B 2
We know |z1−z2|=|z1−(z2−3−4i)−(3+4i)|
≥|z1|−|z23−4i|−|3+4i|
≥12−5−5 , using |z1−z2|≥|z1|−|z2|
∴ |z1−z2|≥2.
2
We know |z1−z2|=|z1−(z2−3−4i)−(3+4i)|
≥|z1|−|z23−4i|−|3+4i|
≥12−5−5 , using |z1−z2|≥|z1|−|z2|
∴ |z1−z2|≥2.
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