First slide

Geometry of complex numbers

Question

The vector $z = 3 - 4 i$ is turned anticlockwise through an angle of $180^{0}$ and stretched 2.5 times. The complex number corresponding to the newly obtained vector is:

Easy

A

$\frac{15}{2} - 10 i$
B

$\frac{- 15}{2} + 10 i$
C

$\frac{- 15}{2} - 10 i$
D

None of these

Solution

$3 - 4 i$ i.e., $(3, - 4)$ lie in fourth quadrant in complex plane, after turned anticlockwise through $180^{0}$ this will lie in II quadrant, therefore, the number will be $- 3 + 4 i$ , now after stretching it 2.5 times i.e., multiplying by 2.5, the required complex number will be $\frac{- 15}{2} + 10 i$ .

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