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Question

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
(12,52)
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B
(12,52)
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C
(12,52)
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D
(12,52)
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Solution

The correct option is D (12,52)
Let zA=2+3i and after rotation the complex number be zB then
|zA|=|zB|
Using rotation property we have
zBzA=|zB||zA|eiπ4zB=zAeiπ4zB=(2+3i)(12+i12)zB=12+52i
Hence required point will be (12,52)

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