A) \[12+9i\]
B) \[12-9i\]
C) \[-12-9i\]
D) \[-12+9i\]
Correct Answer: D
Solution :
\[|z|=\sqrt{{{4}^{2}}+{{(-3)}^{2}}}=5\] Let \[{{z}_{1}}\] be the new vector obtained by rotating \[z\] in the clockwise sense through \[{{180}^{o}}\], therefore \[{{z}_{1}}={{e}^{-i\pi }}z=(\cos \pi -i\sin \pi ),\]i.e., \[z=-4+3i\] The unit vector in the direction of \[{{z}_{1}}\]is \[-\frac{4}{5}+\frac{3}{5}i\] . Therefore required vector \[=3|z|\,\left( -\frac{4}{5}+\frac{3}{5}i \right)=15\left( -\frac{4}{5}+\frac{3}{5}i \right)=-12+9i\]
You need to login to perform this action.
You will be redirected in
3 sec
