Question

The triangle formed by the points 1, $\frac{1+i}{\sqrt{2}}$, $i$ as vertices in the Argand diagram is isosceles. If this is true enter 1, else enter 0.

Answer 1

The vertices of the triangle are $A(1,0)B(1/\sqrt{2},1/\sqrt{2})$, and $C(0,1)$.
Thus, $A{B}^2=2-\sqrt{2},B{C}^2=2-\sqrt{2},A{C}^2=1+1=2$
$\therefore AB=BC$
$⟹$ Triangle is isosceles
Ans: 1