Complex Numbers
Solving complex quadratic equation
nta_pyq_2025_apr
Grade 12
Question:
Let z$\i_n C be such that$z +3i = 2 + 3i$. Then the sum of all possible values of z is 2$z-2$+i$
$19 - 2i$
$-19 - 2i$
$19 + 2i$
$-19 + 2i$
Step-by-Step Solution
Key Concept: $Cross-multiply$the complex equation to obtain a quadratic in$z$, then use Vieta for the sum of roots.
$z + 3i = z(2 + 3i) - 7 - 4i$2$(2)$2$z - z(2 + 3i) + 7 + 7i = 0$2 2 2$z + z = ($$z_{1}$$+ z_{2}$) - 2z1$z_{2}$1$2 = 4 - 9 + 12i - 14 - 14i$= -$19 - 2i$
Correct Answer: 2