Let S be the set of all complex numbers z satisfying $\left|z-2+i\right|\ge\sqrt{5}.$ If the complex number $z_0$ is such that $\frac{ 1}{\left|z_{0}-1\right|}$ is the maximum of the set $\left\{\frac{ 1}{\left|z_{0}-1\right|}: z\,\in\,S\right\},$ then the principal argument of $\frac{4-z_{0}-z^{-}_{0}}{z_{0}-z^{-}_{0}+2i}$ is
- $-\frac{\pi}{2}$
- $\frac{\pi}{4}$
- $\frac{\pi}{2}$
- $-\frac{3\pi}{4}$
The Correct Option is A
Solution and Explanation
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Statement-I: \( z \) is a real number
Statement-II: Principal argument of \( z \) is \( \dfrac{\pi}{3} \)
Then:
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GMC Azamgarh Admission 2025: Dates, Courses, Fees, Eligibility, SelectJuly 22, 2025Concepts Used:
Complex Number
A Complex Number is written in the form
a + ib
where,
- “a” is a real number
- “b” is an imaginary number
The Complex Number consists of a symbol “i” which satisfies the condition i^2 = −1. Complex Numbers are mentioned as the extension of one-dimensional number lines. In a complex plane, a Complex Number indicated as a + bi is usually represented in the form of the point (a, b). We have to pay attention that a Complex Number with absolutely no real part, such as – i, -5i, etc, is called purely imaginary. Also, a Complex Number with perfectly no imaginary part is known as a real number.