1
JEE Main 2020 (Online) 6th September Evening Slot
+4
-1
Let z = x + iy be a non-zero complex number such that $${z^2} = i{\left| z \right|^2}$$, where i = $$\sqrt { - 1}$$ , then z lies on the :
A
line, y = –x
B
real axis
C
line, y = x
D
imaginary axis
2
JEE Main 2020 (Online) 6th September Morning Slot
+4
-1
The region represented by
{z = x + iy $$\in$$ C : |z| – Re(z) $$\le$$ 1} is also given by the
inequality : {z = x + iy $$\in$$ C : |z| – Re(z) $$\le$$ 1}
A
y2 $$\le$$ $$2\left( {x + {1 \over 2}} \right)$$
B
y2 $$\le$$ $${x + {1 \over 2}}$$
C
y2 $$\ge$$ 2(x + 1)
D
y2 $$\ge$$ x + 1
3
JEE Main 2020 (Online) 5th September Evening Slot
+4
-1
The value of $${\left( {{{ - 1 + i\sqrt 3 } \over {1 - i}}} \right)^{30}}$$ is :
A
–215i
B
–215
C
215i
D
65
4
JEE Main 2020 (Online) 5th September Morning Slot
+4
-1
If the four complex numbers $$z,\overline z ,\overline z - 2{\mathop{\rm Re}\nolimits} \left( {\overline z } \right)$$ and $$z-2Re(z)$$ represent the vertices of a square of side 4 units in the Argand plane, then $$|z|$$ is equal to :
A
4$$\sqrt 2$$
B
4
C
2
D
2$$\sqrt 2$$
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