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Question: Answered & Verified by Expert
Let w1 be the point obtained by the rotation of z1=5+4i about the origin through a right angle in the anticlockwise direction, and w2 be the point obtained by the rotation of z2=3+5i about the origin through a right angle in the clockwise direction. Then the principal argument w1-w2 is equal to
MathematicsComplex NumberJEE MainJEE Main 2023 (11 Apr Shift 1)
Options:
  • A π-tan-189
  • B -π+tan-1335
  • C -π+tan-189
  • D π-tan-1335
Solution:
1520 Upvotes Verified Answer
The correct answer is: π-tan-189

Given,

Two complex numbers w1 & w2

w1=3+5i and w2=5+4i are both rotated by 90° with respect to origin anticlock-wise and clockwise respectively,

So by concept of rotation we get,

w3=iw1=i3+5i=-5+3i

And w4=-iw2=-i5+4i=4-5i

Now principal argument of w3-w4=-9+8i will be π-tan-189 {as complex number is in second quadrant so principal argument is given by π-tan-1yx}

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