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JEE Advanced 2008Paper 2
Exam
JEE Advanced
Year
2008
Paper
Paper 2
Subject
Mathematics
Chapter
Complex Number

JEE Advanced 2008 · Paper 2 · Mathematics · Complex Number

A particle P starts from the point z_0=1+2 i , where i= -1 . It...

A particle PP starts from the point z0=1+2iz_0=1+2 i, where i=−1i=\sqrt{-1}. It moves first horizontally away from origin by 5 units and then vertically away from origin by 3 units to reach a point z1z_1. From z1z_1 the particle moves 2\sqrt{2} units in the direction of the vector i^+j^\hat{\mathbf{i}}+\hat{\mathbf{j}} and then it moves through an angle π2\frac{\pi}{2} in anti-clockwise direction on a circle with centre at origin, to reach a point z2z_2. The point z2z_2 is given byA particle P starts from the point z_0=1+2 i , where i= -1 . It moves first horizontally away from origin by 5 unitsA particle P starts from the point z_0=1+2 i , where i= -1 . It moves first horizontally away from origin by 5 units

Options

  1. A6+7i6+7 i
  2. B−7+6i-7+6 i
  3. C7+6i7+6 i
  4. D−6+7i-6+7 i

Correct answer

D. −6+7i-6+7 i

Step-by-step solution

A particle P starts from the point z_0=1+2 i , where i= -1 . It moves first horizontally away from origin by 5 units
z_2^{\prime}=\left(6+2×cos⁡\sqrt{2} \times \cos45^{{}^{\circ}}, 5+2sin⁡\sqrt{2} \sin45^{{}^{\circ}}\right)=(7,6)=7+6 i By rotation about (0,0)(0,0),z2z2′=eiπ2⇒z2=z2′(eiπ2)⇒z2=(7+6i)(cos⁡π−+isin⁡π−)=(7+6i)(i)=−6+7i\begin{aligned}& \frac{z_2}{z_2^{\prime}}=e^{i \frac{\pi}{2}} \\ & \Rightarrow \quad z_2=z_2^{\prime}\left(e^{i \frac{\pi}{2}}\right) \\ & \Rightarrow \quad z_2=(7+6 i)\left(\cos \frac{\pi}{-}+i \sin \frac{\pi}{-}\right)=(7+6 i)(i)=-6+7 i \end{aligned}
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