JEE Advanced 2013 Paper 2 Offline | Complex Numbers Question 21 | Mathematics

JEE Advanced 2013 Paper 2 Offline

MCQ (More than One Correct Answer)

-1

Let $\omega=\frac{\sqrt{3}+i}{2}$ and $P=\left\{\omega^n: n=1,2,3, \ldots\right\}$. Further

$\mathrm{H}_1=\left\{z \in \mathrm{C}: \operatorname{Re} z<\frac{1}{2}\right\}$ and

$\mathrm{H}_2=\left\{z \in \mathrm{C}: \operatorname{Re} z<\frac{-1}{2}\right\}$, where C is the

set of all complex numbers. If $z_1 \in \mathrm{P} \cap \mathrm{H}_1, z_2 \in$ $\mathrm{P} \cap \mathrm{H}_2$ and O

represents the origin, then $\angle z_1 \mathrm{O} z_2=$

$${\pi \over 2}$$

$${\pi \over 6}\,$$

$${{2\pi } \over 3}$$

$${{5\pi } \over 6}$$

IIT-JEE 2010 Paper 1 Offline

MCQ (More than One Correct Answer)

-1

Let $${{z_1}}$$ and $${{z_2}}$$ be two distinct complex number and let z =( 1 - t)$${{z_1}}$$ + t$${{z_2}}$$ for some real number t with 0 < t < 1. IfArg (w) denote the principal argument of a non-zero complex number w, then

$$\left| {z - {z_1}} \right| + \left| {z - {z_2}} \right| = \left| {{z_1} - {z_2}} \right|$$

Arg $$(z - {z_1})$$ = Arg$$(z - {z_2})$$

$$\left| {\matrix{ {z - {z_1}} & {\overline z - {{\overline z }_1}} \cr {{z_2} - {z_1}} & {{{\overline z }_2} - {{\overline z }_1}} \cr } } \right|$$ = 0

Arg $$(z - {z_1})$$ = Arg$$({z_2} - {z_1})$$

IIT-JEE 1998

MCQ (More than One Correct Answer)

-0.5

If $$\,\left| {\matrix{ {6i} & { - 3i} & 1 \cr 4 & {3i} & { - 1} \cr {20} & 3 & i \cr } } \right| = x + iy$$ , then

x = 3, y = 2

x = 1, y = 3

x = 0, y = 3

x = 0, y = 0

IIT-JEE 1998

MCQ (More than One Correct Answer)

-0.5

The value of the sum $$\,\,\sum\limits_{n = 1}^{13} {({i^n}} + {i^{n + 1}})$$ , where i = $$\sqrt { - 1} $$, equals

i - 1

- i

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