Question:
If \(A, B, C\) are the angles of a triangle and
\[
e^{iA}, \; e^{iB}, \; e^{iC}
\]
are in A.P., then the triangle must be
If \(A, B, C\) are the angles of a triangle and
\[ e^{iA}, \; e^{iB}, \; e^{iC} \]
are in A.P., then the triangle must be
\[ e^{iA}, \; e^{iB}, \; e^{iC} \]
are in A.P., then the triangle must be
Show Hint
Symmetry in complex exponentials often implies equality of angles.
Updated On: Mar 23, 2026
- right angled
- isosceles
- equilateral
- none of these
Show Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Step 1: A.P. condition: 2eⁱB=eⁱA+eⁱC.
Step 2: This implies A=B=C.
Step 3: Hence the triangle is equilateral.
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