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Question

A complex number z=3+4i is rotated about another fixed complex number z1=1+2i in anticlockwise direction by 45o angle. Find the complex number represented by new position of z in argand plane

A
1+(22)i
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B
1+(2+22)i
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C
1(2+22)i
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D
1+(2+2)i
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Solution

The correct option is A 1+(2+22)i
A complex number when multiplied by eiθ is rotated by θ in the anticlockwise direction.
Here, since the point about which the complex number has to be rotated is not origin, we need to subtract the fixed point from the given complex number.
So, the new z after rotation =(3+4i12i)×eiπ4+(1+2i)
z=(2+2i)×(12+i12)+(1+2i)
z=22i+1+2i=1+i(2+22)

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