Question

# If z=√2−i√2 is rotated through an angle 45° in the anti-clockwise direction about the origin, then the coordinates of its new position are  [Kerala (Engg.) 2005]

A

(2, 0)

B

(2,2)

C

(2,2)

D
(2,0
E
(4, 0)

Solution

## The correct option is E (√2,0z=√2−i√2 Here, θ=tan−1=(−√2√2)=tan−1(−1)=135o Now, rotate z in opposite direction with 45° angle ∴ θ=180o ∴ θ=tan0=tan−1(0√2) ⇒ Hence x=√2 and y=0. Mathematics

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