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Question

The complex number z2(2 + 3i) is rotated through an angle of 90 anti-clockwise about z1(1 + i). Find the new complex number z3 obtained.


  1. 1 + 2i

  2. 1-2i

  3. -1 + 2i

  4. -1 -2i


Solution

The correct option is C

-1 + 2i


Here, we will apply the concept of rotation.

It gives us the relation between the complex numbers z1,z2and z3, which are connected like in the figure.

The following relation can be used to find the any of the complex number, when other two and the angle are given.

We can also find the angle using this relation.

z3z1z2z1  = z3z1z2z1 eiπ2


z3z1 = (z2z1 ) × eiπ2
z3 - (1+i) = (2+3i -(1+i)) i

        = (1+2i)i

z3 - (1+i) = i - 2

z3 = 1+i+(i-2)

= -1+2i

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