Question

Among the complex number $z$, satisfying the condition $|z+1-i|\le 1$, the number having the least positive argument is-

• A. $1-i$
• B. $-1+i$
• C. $-i$
• D. none of these

Answer 1

The correct option is D none of these

Given $|z+1-i|\le 1⟶\left(1\right)$

$\Rightarrow z=1-i$

Substitute in $\left(1\right)$

$\Rightarrow |1-i+1-i|\nleqq 1$

Does not satisfy

$\Rightarrow$ Put $z=-1+i$ in $\left(1\right)$

$|-1+i+1-i|\le 1$

argument of $z=\frac{-\Pi }{4}$

$\Rightarrow$ Put $z=-i$

$|-i+1-i|\nleqq 1$

Does not satisfy

Hence, the answer is none of these.