Let $z \in C$ with Im(z) = 10 and it satisfies $\frac{2z-n}{2z+n} = 2i -1$ for some natural number $n$.Then :
- n = 20 and Re(z) = - 10
- n = 20 and Re(z) = 10
- n = 40 and Re(z) = - 10
- n = 40 and Re(z) = 10
The Correct Option is C
Solution and Explanation
$\therefore 2(x + 10i) - n = (2i - 1) . [2(x+10i) + n]$
compare real and imaginary coefficients
$x = - 10, n = 40$
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Concepts Used:
Complex Numbers and Quadratic Equations
Complex Number: Any number that is formed as a+ib is called a complex number. For example: 9+3i,7+8i are complex numbers. Here i = -1. With this we can say that i² = 1. So, for every equation which does not have a real solution we can use i = -1.
Quadratic equation: A polynomial that has two roots or is of the degree 2 is called a quadratic equation. The general form of a quadratic equation is y=ax²+bx+c. Here a≠0, b and c are the real numbers.
