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Question
State True or False for the following:
For any complex number z the minimum value of |z| + |z – 1| is 1.
Options
True
False
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Solution
This statement is True.
Explanation:
Let z = x + yi
∴ |z| + |z – 1| = `sqrt(x^2 + y^2) + sqrt((x - 1)^2 + y^2)`
The value of |z| + |z – 1| is minimum, When x = 0, y = 0 i.e., 1.
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