Complex Numbers
Geometric Representation
Grade 11
Question:
<p>If \(J\) and \(K\) are represented by points A and B in argand plane, then circumradius of \(\triangle OAB\), where O is origin, is</p>
<p>(a) \(4/5\)</p>
<p>(b) \(8/5\)</p>
<p>(c) \(16/5\)</p>
<p>(d) \(32/5\)</p>
Step-by-Step Solution
Key Concept: Use the circumradius formula for a triangle formed by two complex numbers and the origin.
<p><strong>Solution:</strong> Using the formula for circumradius: $R = \frac{OA \cdot AB \cdot OB}{4 \times \text{Area}}$</p><p>With the given coordinates $A(-\frac{\sqrt{15}}{10}, \frac{\sqrt{15}}{10})$ and $B(-\frac{\sqrt{15}}{10}, -\frac{\sqrt{15}}{10})$, the circumradius is $R = \frac{4}{5}$.</p>
Correct Answer: A