Complex Numbers
Rotation of Complex Numbers
Premium Question
Grade 11
Question:
The point $C$ is obtained by rotating $B$ about $A$ by $90^\circ$ anticlockwise. If $z_A = 1 + i$ and $z_B = 3 + 2i$, then $z_C$ equals:
(1) $-1 + 3i$
(2) $3i$
(3) $i$
(4) $1 + 4i$
Step-by-Step Solution
Key Concept: Use the rotation formula: $z_C - z_A = (z_B - z_A) \cdot e^{i\pi/2} = (z_B - z_A) \cdot i$. Compute $z_B - z_A$ first, multiply by $i$, then add $z_A$.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (1)