1
JEE Advanced 2018 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1
For a non-zero complex number z, let arg(z) denote the principal argument with $$-$$ $$\pi $$ < arg(z) $$ \le $$ $$\pi $$. Then, which of the following statement(s) is (are) FALSE?
A
arg($$-$$1$$-$$i) = $${\pi \over 4}$$, where i = $$\sqrt { - 1} $$
B
The function f : R $$ \to $$ ($$-$$$$\pi $$, $$\pi $$), defined by f(t) = arg ($$-$$1 + it) for all t $$ \in $$ R, is continuous at all points of R, where i = $$\sqrt { - 1} $$.
C
For any two non-zero complex numbers z1 and z2, arg $$\left( {{{{z_1}} \over {{z_2}}}} \right)$$$$-$$ arg (z1) + arg(z2) is an integer multiple of 2$$\pi $$.
D
For any three given distinct complex numbers z1, z2 and z3, the locus of the point z satisfying the condition arg$$\left( {{{(z - {z_1})({z_2} - {z_3})} \over {(z - {z_3})({z_2} - {z_1})}}} \right) = \pi $$, lies on a straight line.
2
JEE Advanced 2017 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1
Let a, b, x and y be real numbers such that a $$-$$ b = 1 and y $$ \ne $$ 0. If the complex number z = x + iy satisfies $${\mathop{\rm Im}\nolimits} \left( {{{az + b} \over {z + 1}}} \right) = y$$, then which of the following is(are) possible value(s) of x?
A
$$1 - \sqrt {1 + {y^2}} $$
B
$$ - 1 - \sqrt {1 - {y^2}} $$
C
$$1 + \sqrt {1 + {y^2}} $$
D
$$ - 1 + \sqrt {1 - {y^2}} $$
3
JEE Advanced 2016 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-2
Let $$a,\,b \in R\,and\,{a^{2\,}} + {b^2} \ne 0$$. Suppose
$$S = \left\{ {Z \in C:Z = {1 \over {a + ibt}}, + \in R,t \ne 0} \right\}$$, where $$i = \sqrt { - 1} $$. Ifz = x + iy and z $$ \in $$ S, then (x, y) lies on
A
the circle with radius $${{1 \over {2a}}}$$and centre $$\left\{ {{1 \over {2a}},\,0} \right\}\,for\,a > 0\,,b \ne \,0$$
B
the circle with radius $$-{{1 \over {2a}}}$$and centre $$\left\{ -{{1 \over {2a}},\,0} \right\}\,for\,a < 0\,,b \ne \,0$$
C
the x-axis for $$a \ne \,\,0,\,b \ne \,0$$
D
the y-axis for $$a = \,\,0,\,b \ne \,0$$
4
JEE Advanced 2013 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-1
Let $$w = {{\sqrt 3 + i} \over 2}$$ and P = { $${w^n}$$ : n = 1, 2, 3, ...}. Further JEE Advanced 2013 Paper 2 Offline Mathematics - Complex Numbers Question 46 English 1 and JEE Advanced 2013 Paper 2 Offline Mathematics - Complex Numbers Question 46 English 2, where is the set of all complex numbers. If $${z_1} \in P \cap {H_1},\,{z_2} \in \,P \cap {H_2}$$ and 0 represents the origin, then $$\angle \,{z_1}\,o{z_2} = $$
A
$${\pi \over 2}$$
B
$${\pi \over 6}\,$$
C
$${{2\pi } \over 3}$$
D
$${{5\pi } \over 6}$$
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