Given that a complex number A = 1 + i, we need to find the complex number B that lies in the 2nd quadrant, such that on the Argand Diagram, the points O, B and A form an equilateral triangle (where O is the origin).
To make sense of what this is saying, we need to first draw a diagram - an Argand Plane. We first note that A has the coordinates (1,1); O has the coordinates (0,0) and let's give B the coordinates (x,y), which we have to solve.
We then use the polar form of complex number multiplication to find a point B(x,y) that forms an equilateral triangle with the point A(1,1) and the origin O(0,0).
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