Prove that the triangle formed by the points `1,(1+i)/(sqrt(2))`,and `i` as vertices in the Argand diagram is isosceles.

Explanation

The vertical of the triangle are `A(1),B ((1+i)/(sqrt(2)))` and C(i). i.e., vertical of the triangle are` A(1,0)B ((1)/(sqrt(2)),(1)/(sqrt(2)))` and C(0,1)
`therefore " "AB^(2)=(1-(1)/(sqrt(2)))^(2) + (0-(1)/sqrt(2))^(2) = 2 - sqrt(2)`
`BC^(2) =((1)/sqrt(2) -0)^(2) + ((1)/sqrt(2) -1)^(2) = 2 -sqrt(2)`
Thus, AB= BC
So, triangle is isosceles.