Complex Numbers
Complex Numbers
star_batch_jee_advanced_2025
Grade 11
Question:
If $k \in \mathbb{R} - \{0\}$, $z$ is a complex number and $k + |k + z^2| = |z^2|$ then the value of $\arg z$ is/are
$-\pi$
$-\frac{\pi}{2}$
$\frac{\pi}{2}$
$\pi$
Step-by-Step Solution
Key Concept: Extract coefficients from polynomial expansion by carefully tracking powers of x from each factor.
The required number of selections of 4 letters is the coefficient of $x^4$ in the expansion of $(x^0 + x^1)(x^0 + x)(x + x^2)(x^0 + x^1 + x^2)(x^0 + x^1) = (1 + x)^2(1 + x + x^2)^2 = 18$.
Correct Answer: 2,3