# Pure Mathematics

posted by
**Queenie**
.

1)

i) use an algrbraic method to find the square root of 2+i√5. give your answer in the form x+iy, where x and y are exact real numbers

ii)hence find in the form x+iy where x and y are exact real numbers, the roots of the equation z^4-4z^2+9=0

iii) show those roots on an argand diagram (part ii)

iv) given that α is a root of the equation in part (ii) such that 0< or equal to argα< or equal to π/2, sketch on the same argand diagram the locus of |z-α|=|z|