JEE Main 2024 Mathematics question
If z = x + iy, xy ≠ 0, satisfies the equation z² + i z̄ = 0, then |z²| is equal to :
Answer: (C)
Solution
z² = −i z̄, so |z|² = |z̄| = |z|. Since |z| ≠ 0 (xy ≠ 0), |z| = 1 and |z²| = |z|² = 1.
If z = x + iy, xy ≠ 0, satisfies the equation z² + i z̄ = 0, then |z²| is equal to :
z² = −i z̄, so |z|² = |z̄| = |z|. Since |z| ≠ 0 (xy ≠ 0), |z| = 1 and |z²| = |z|² = 1.