Complex Numbers
Geometry of Complex Numbers
Premium Question
Grade 11
Question:
Find the complex number $z$ satisfying $|z| = |z - 1| = |z - i|$:
(1) $\frac{1 + i}{2}$
(2) $1 + i$
(3) $\frac{1 - i}{2}$
(4) $\frac{1 + i}{\sqrt{2}}$
Step-by-Step Solution
Key Concept: $|z| = |z - 1|$ gives the perpendicular bisector of $0$ and $1$; $|z - 1| = |z - i|$ gives the perpendicular bisector of $1$ and $i$. Find their intersection.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (1)