QJEEAdv08Ma358c: JEE Advanced 2008 Mathematics - Class 11 JEEAdv08Ma358c Solution: A particle P stats from the point = 1 +2i, where . It moves…

Question

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A particle P stats from the point

{z_0}

= 1 +2i, where

i = \sqrt { - 1}

. It moves horizontally away from origin by 5 unit and then vertically away from origin by 3 units to reach a point

{z_1}

. From

{z_1}

the particle moves

\sqrt 2

units in the direction of the vector

\hat i + \hat j

and then it moves through an angle

{\pi \over 2}

in anticlockwise direction on a circle with centre at origin, to reach a point

{z_2}

. The point

{z_2}

is given by

Accepted Answer

given $-$ $\alpha$ particle

In the direction of, or, Now rotation about origin through angle of means multiply by

${z_0} = 1 + 2i = (1,2) = ({x_0},{y_0})$

${z_1} = ({x_0} + 5,{y_0} + 3)$

$= (6,5) = 6 + 5i$

$\Rightarrow 2$ in the direction of $i = j$

${x_1} = 2\cos 45^\circ$

${y_1} = 2\sin 45^\circ$

${z_2}(7 + 6i)$

Now, rotation about origin through an angle of 2 $\pi$ means multiply z $_2$ by $\to {e^{i\pi /2}}$

$\cos 90^\circ + i\sin 90^\circ = i$

${z_3} = i(7 + 6i)$

$= - 6 + 7i$

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