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Question

A particle starts from a point z0=1+i, where i=i. It moves horizontally away from origin by 2 units and then vertically away from origin by 3 units to reach a point z1. From z1 particle moves 5 units in the direction of 2^i+^j and then it moves through an angle of cosec12 in anticlockwise direction of a circle with centre at origin to reach a point z2. The argz2 is given by

A
sec12
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B
cot10
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C
sin1(3122)
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D
cos1(12)
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Solution

The correct option is B cot10
From the graph,
arg(z1)=tan1(5/5)=45
cosec 12=45
Since, z1 moves through by an angle 45 in anti-clockwise direction.
The angle made by z2 with axis will be 45+45=90
arg(z2)=90=cot10

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