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Question

In the Argand plane, the vector z=4-3i is turned in the clockwise sense through 180o and stretched three times. The complex number represented by the new vector is


A

12+9i

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B

12-9i

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C

-12-9i

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D

-12+9i

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Solution

The correct option is D

-12+9i


|z|=42+()2=5

Let z1 be the new vector obtained by rotating

z in the the clockwise sense through 180,

therefore

z1=eiπz=(cosπ-isinπ), i.e., z=-4+3i

The unit vector in the direction of z1 is (45+35i)

Therefore 3|z|(45+35i)=15(45+35i)=-12+9i


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