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$Complex number z satisfies | z - a + i a | = 1 and has the least$ $absolute value. Its absolute value is$

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$a \sqrt{2} - 1$

$a \sqrt{2} + 1$

answer is A.

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Detailed Solution

$\begin{array}{l} |z - z_{0}| = r, represents a circle so the least modulus of z is |z_{0}| - r \\ ∴ The least absolute value of z = |a (1 - i)| -1 \\ = a \sqrt{2} - 1 \end{array}$

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