MHT CET · Maths · Complex Number
A particle \(P\) starts from the point \(Z_0=1+2 i\) where \(i=\sqrt{-1}\). It moves first horizontally away from the origin by 5 units and then vertically upwards parallel to positive \(y\)-axis by 3 units to reach a point \(Z_1\). From \(Z_1\) the particle moves \(\sqrt{2}\) units in the direction of vector \(\hat{i}+\hat{j}\) and then it moves through an angle \(\frac{\pi}{2}\) in anticlockwise direction on a circle with centre at origin to reach at point \(Z_2\), then \(Z_2=\)
- A \(6+7 i\)
- B \(-7+6 i\)
- C \(-6+7 i\)
- D \(7-6 i\)
Answer & Solution
Correct Answer
(C) \(-6+7 i\)
Step-by-step Solution
Detailed explanation
\(Z_1 = (1+5)+ (2+3)i = 6+5i\) \(Z_1' = Z_1 + \sqrt{2} \left( \frac{1+i}{\sqrt{1^2+1^2}} \right) = 6+5i + (1+i) = 7+6i\)
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