Multiplication of complex number by $~i~/-i~$ 
Multiplication of non-zero complex number with $~-i~$ rotates the point about origin through a right angle in anticlockwise direction. True or false? 

My attempt :- actually I don't know how to proceed in general but I did it with an example of $~1+i~$ and by multiplying it with $~-i~$  the point turns $~ 90~$ in clockwise direction. Also if we multiple the above complex number by $~i~$  it rotates by $~90~$ in anti-clockwise direction.  Is the above result is true in general of just for particular example. 
Also general proof will be appreciated.  Thanks 
 A: I assume that by “anticlockwise” you mean “with the same verse of rotation by which the positive $x$-semiaxis reaches the positive $y$-axis by the least angle”; “clockwise” is the opposite verse of rotation.
Then multiplication by $-i$ induces a clockwise rotation by a right angle, because $1\cdot(-i)=-i$, which in the standard representation of complex numbers has a negative $y$-coordinate.
As you see, there are many implicit assumptions in the statement of the problem.
If you decide to represent the $x$-axis in the usual fashion (horizontal, positive verse from left to right) and the $y$-axis upside down with respect to the usual way, then, with the intuitive understanding of clockwise and anticlockwise, multiplication by $-i$ induces an anticlockwise rotation by a right angle. That's why I initially gave a definition that's independent on the graphical representation.
Another case: suppose your teacher is drawing on a side of a transparent board and you're on the opposite side; you and the teacher will see different verses of rotation, under the common understanding of clockwise ad anticlockwise. Not if you stick to the definition I gave.
By the way, the “anticlockwise” verse I defined at the top is usually and better called positive.
A: It's easy to see in general, by drawing in the coordinate system. The complex number $a+bi$ is represented as (the vector from the origin to) the point with coordinates $(a, b)$.
We have
$$(a+bi)\cdot i=-b+ai\\
(a+bi)\cdot(-i)=b-ai$$
A: This is wrong. Usually one puts the unit $i$ on the vertical coordinate axis in upright position, so that to go from $1$ to $i$ is an anti-clockwise rotation by $90°$. Then $-i$ is in the downward position and multiplication by $-i$ rotates by $90°$ in clockwise direction. Remember that $1=1+0i$ is at the 3:00 position on the clock, $i$ at the 12:00 position and $-i$ at the 6:00 position.
