1
IIT-JEE 1983
MCQ (Single Correct Answer)
+1
-0.25
If $$z = x + iy$$ and $$\omega = \left( {1 - iz} \right)/\left( {z - i} \right),$$ then $$\,\left| \omega \right| = 1$$ implies that, in the complex plane,
A
$$z$$ lies on the imaginary axis
B
$$z$$ lies on the real axis
C
$$z$$ lies on the unit circle
D
none of these
2
IIT-JEE 1983
MCQ (Single Correct Answer)
+1
-0.25
The points z1, z2, z3, z4 in the complex plane are the vertices of a parallelogram taken in order if and only if
A
z1 + z4 = z2 + z3
B
z1 + z3 = z2 + z4
C
z1 + z2 = z3 + z4
D
None of these
3
IIT-JEE 1983
Subjective
+3
-0
Prove that the complex numbers $${{z_1}}$$, $${{z_2}}$$ and the origin form an equilateral triangle only if $$z_1^2 + z_2^2 - {z_1}\,{z_2} = 0$$.
4
IIT-JEE 1983
Subjective
+2
-0
Find all solutions of $$4{\cos ^2}\,x\sin x - 2{\sin ^2}x = 3\sin x$$
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