Question

If $ z=\sqrt{2}-i\sqrt{2} $ is rotated through an angle $ 45{}^\circ $ in the anticlockwise direction about the origin, then the co-ordinates of its new position are:

• A. $ (2,0) $
• B. $ (\sqrt{2},\sqrt{2}) $
• C. $ (\sqrt{2},-\sqrt{2}) $
• D. $ (\sqrt{2},0) $
• E. $ (4,0) $

Answer 1

Answer: (A)

$ {{z}_{2}}=z{{e}^{i\pi /4}} $
$ =(\sqrt{2}-i\sqrt{2})(\cos \pi /4+i\sin \pi /4) $
$ =\sqrt{2}(1-i)\frac{(1+i)}{\sqrt{2}} $
$ =1-{{i}^{2}}=1+1=2+0i $
$ \therefore $ Co-ordinate of new position are (2, 0).