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Addition of Vectors

The vector z ...

Question

The vector z=3-4i is turned anticlockwise through an angle of $180^{\circ}$ and stretched 2.5 times. The complex number corresponding to the newly obtained vector is

-10i

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+10i

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-10i

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None of these

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Solution

The correct option is B
+10i

3-4i i.e., (3,-4) lie in fourth quadrant in complex plane, after turned anticlock through $180^{\circ}$ this will lie in II quadrant, therefore, the number will be -3+4i, now after streching it 2.5 times i.e., multiplying by 2.5, the required complex number will be $\frac{- 15}{2}$ +10i.

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The vector z=3-4i is turned anticlockwise through an angle of 180∘ and stretched 2.5 times. The complex number corresponding to the newly obtained vector is

The correct option is B +10i 3-4i i.e., (3,-4) lie in fourth quadrant in complex plane, after turned anticlock through 180∘ this will lie in II quadrant, therefore, the number will be -3+4i, now after streching it 2.5 times i.e., multiplying by 2.5, the required complex number will be −152+10i.

The vector z=3-4i is turned anticlockwise through an angle of $180^{\circ}$ and stretched 2.5 times. The complex number corresponding to the newly obtained vector is