arg($$-$$1$$-$$i) = $${\pi \over 4}$$, where i = $$\sqrt { - 1} $$

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 = $$\sqrt { - 1} $$.

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$$\pi $$.

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.

$$\angle QPR = 45^\circ $$

The area of the $$\Delta PQR$$ is $$25\sqrt 3 $$ and $$\angle QRP = 120^\circ $$

The radius of the incircle of the $$\Delta PQR$$ is $$10\sqrt 3 $$ $$-$$ 15

The area of the circumcircle of the $$\Delta PQR$$ is 100$$\pi $$

The line of intersection of P₁ and P₂ has direction ratios 1, 2, $$-$$1

The line $${{3x - 4} \over 9} = {{1 - 3y} \over 9} = {z \over 3}$$ is perpendicular to the line of intersection of P₁ and P₂

The acute angle between P₁ and P₂ is 60$$^\circ $$

If P₃ is the plane passing through the point (4, 2, $$-$$2) and perpendicular to the line of intersection of P₁ and P₂, then the distance of the point (2, 1, 1) from the plane P₃ is $${2 \over {\sqrt 3 }}$$

There exist r, s $$ \in $$ R, where r < s, such that f is one-one on the open interval (r, s)

There exists x₀ $$ \in $$ ($$-$$4, 0) such that |f'(x₀)| $$ \le $$ 1

$$\mathop {\lim }\limits_{x \to \infty } f(x) = 1$$

There exists $$\alpha $$$$ \in $$($$-$$4, 4) such that f($$\alpha $$) + f"($$\alpha $$) = 0 and f'($$\alpha $$) $$ \ne $$ 0