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
-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=e−iπz=(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