Complex Numbers
Complex Numbers
nta_abhyas_2025
Grade 11
Question:
If $P(z)$ is a variable point in the complex plane such that $\tan\left(-\frac{1}{z}\right) = \frac{1}{2}$, then the value of the perimeter of the locus of $P(z)$ is (use $\pi = 3.14$)
Step-by-Step Solution
Key Concept: Complex number equality requires both real and imaginary parts to be equal separately
Given: $\frac{(1-x)(1-2)}{3x+1} - \frac{0}{3x+1} = i$. Simplifying: $\frac{(1-y)(1-3)}{3x+1} - \frac{(1-2)(3)(+3x+3)}{(x+1)} = i$. Computing the numerator and denominator, we get $\frac{(1-y)(1-3) - 26(3+3x+3)}{(x+1)} = i$, which yields $y = -1$.
Correct Answer: 3