Question

Let z=1a+i(a^2+a+2)^1/2, where a' is a real parameter. Find the locus of z in argand plane.

Answer 1

Z = a + i√(a²+a+2)

Let Z = x +iy

x = a

y = √a²+a+2 = √x²+x+2

∴ The required locus is y² = x²+x+2