1
IIT-JEE 1979
Subjective
+2
-0
If x + iy = $$\sqrt {{{a + ib} \over {c + id}}} $$, prove that $${({x^2} + {y^2})^2} = {{{a^2} + {b^2}} \over {{c^2} + {d^2}}}$$.
2
IIT-JEE 1978
Subjective
+2
-0
If x = a + b, y = a$$\gamma $$ + b$$\beta $$ and z = a$$\beta $$ +b$$\gamma $$ where $$\gamma $$ and $$\beta $$ are the complex cube roots of unity, show that xyz = $${a^3} + {b^3}$$.
3
IIT-JEE 1978
Subjective
+2
-0
Express $${1 \over {1 - \cos \,\theta + 2i\sin \theta }}$$ in the form x + iy.
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