If z = x + iy satisfies | z | – 2 = 0 and |z – i| – | z + 5i| = 0, then
- x + 2y – 4 = 0
x2 + y – 4 = 0
- x + 2y + 4 = 0
x2 – y + 3 = 0
The Correct Option is C
Solution and Explanation
The correct answer is (C) : x + 2y + 4 = 0
|z-i| = |z+5i|
Thereafter, z lies on ⊥r bisector of (0, 1) and (0, –5)
i.e., line y = –2
as |z| = 2
⇒ z = –2i
x = 0 and y = –2Hence, x + 2y + 4 = 0
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Concepts 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.