Form polynomial equations of the lowest degree , with roots as given below
`1pm 2i, 4,2
Hint : In an equation Imaginary roots occur in conjugate pairs.

Explanation

Equation having roots `alpha ,beta, gamma,delta is (x-alpha) (x-beta) (x-gamma) (x-delta)=0`
Required equation is
`[x-(1+2i)] [x-(1-2i)](x-4)(x-2)=0`
= [(x-1)-2i] [(x-1) +2i]
`=(x-1)^2-4i^2 `
=`(x-1)^2+4 `
`x^2 -2x+1+4`
`x^2-2x+5`
`(x-4) (x-2)=x^2 -4x 2x+8`
=`x^2=6x+8 `
Required equation
`(x^2-2x+5) (x^2-6x+8)=0`
`rArr x^4 -2x^3 +5x^2-6x^3+12x2-30x+8x^2-16x+40 =0`
`rArr x^4 -8x^3+25x^2-46x+40=0`