If a point in argand plane A(2,3) rotated through origin about π4 in anticlockwise, then new coordinates of the point will be
A
(1√2,−5√2)
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B
(−1√2,−5√2)
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C
(1√2,5√2)
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D
(−1√2,5√2)
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Solution
The correct option is D(−1√2,5√2) Let zA=2+3i and after rotation the complex number be zB then |zA|=|zB| Using rotation property we have zBzA=|zB||zA|eiπ4⇒zB=zAeiπ4⇒zB=(2+3i)(1√2+i1√2)∴zB=−1√2+5√2i Hence required point will be (−1√2,5√2)