cmi-entrance 2013 QA7

cmi-entrance · India · ugmath 5 marks Complex numbers 2 Roots of Unity and Cyclotomic Properties

Let $A , B , C$ be angles such that $e ^ { i A } , e ^ { i B } , e ^ { i C }$ form an equilateral triangle in the complex plane. Find values of the given expressions. a) $e ^ { i A } + e ^ { i B } + e ^ { i C }$
Answer: $\_\_\_\_$ b) $\cos A + \cos B + \cos C$
Answer: $\_\_\_\_$ c) $\cos 2 A + \cos 2 B + \cos 2 C$
Answer: $\_\_\_\_$ d) $\cos ^ { 2 } A + \cos ^ { 2 } B + \cos ^ { 2 } C$
Answer: $\_\_\_\_$

Let $A , B , C$ be angles such that $e ^ { i A } , e ^ { i B } , e ^ { i C }$ form an equilateral triangle in the complex plane. Find values of the given expressions.\\
a) $e ^ { i A } + e ^ { i B } + e ^ { i C }$

Answer: $\_\_\_\_$\\
b) $\cos A + \cos B + \cos C$

Answer: $\_\_\_\_$\\
c) $\cos 2 A + \cos 2 B + \cos 2 C$

Answer: $\_\_\_\_$\\
d) $\cos ^ { 2 } A + \cos ^ { 2 } B + \cos ^ { 2 } C$

Answer: $\_\_\_\_$

Paper Questions

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