IIT-JEE 2007 Paper 1 Offline | Complex Numbers Question 44 | Mathematics

IIT-JEE 2007 Paper 1 Offline

MCQ (Single Correct Answer)

-1

A man walks a distance of 3 units from the origin towards the north-east (N 45$$^\circ$$E) direction. From there, he walks a distance of 4 units towards the north-west (N 45$$^\circ$$W) direction to reach a point P. Then the position of P in the Argand plane is

$$3{e^{i\pi /4}} + 4i$$

$$(3 - 4i){e^{i\pi /4}}$$

$$(4 + 3i){e^{i\pi /4}}$$

$$(3 + 4i){e^{i\pi /4}}$$

IIT-JEE 2006

MCQ (Single Correct Answer)

-1

If $$w=\alpha+\mathrm{i} \beta$$, where $$\beta \neq 0$$ and $$z \neq 1$$, satisfies the condition that $$\left(\frac{w-\bar{w} z}{1-z}\right)$$ is purely real, then the set of values of $$z$$ is:

$$\{z:|z|=1\}$$

$$\{z: z=\vec{z}\}$$

$$\{z: z \neq z\}$$

$$\{z:|z|=1, z \neq 1 \mid\}$$

IIT-JEE 2006

MCQ (Single Correct Answer)

-1

If $P$ is a point on $C_1$ and $Q$ in another point on $\mathrm{C}_2$, then $\frac{\mathrm{PA}^2+\mathrm{PB}^2+\mathrm{PC}^2+\mathrm{PD}^2}{\mathrm{QA}^2+\mathrm{QB}^2+\mathrm{QC}^2+\mathrm{QD}^2}$ is equal to :

0.75

1.25

0.5

IIT-JEE 2005 Screening

MCQ (Single Correct Answer)

-0.5

$$a,\,b,\,c$$ are integers, not all simultaneously equal and $$\omega $$ is cube root of unity $$\left( {\omega \ne 1} \right),$$ then minimum value of $$\left| {a + b\omega + c{\omega ^2}} \right|$$ is

$${{\sqrt 3 } \over 2}$$

$${1 \over 2}$$

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