1)

Question

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|

Answer 1

2+i√5 = 1/4 (8+4i√5) = 1/4 (10+4i√5-2) = 1/4 (√10+i√2)^2
so √(2+i√5) = 1/2 (√10+√2i)

The rest should fall right out.

Answer 2

I don't understand how you got any of that =(

Answer 3

where'd the 1/4 and all that come from?