Please with clearly written answer Thank you so much If iz2

Please with clearly written answer

Thank you so much

Solution

As z = x +iy where x and y are real numbers

z² = x²+y²+2xyi

iz²= x -iy

i(x²+y²+2xyi) = x -iy

-2xy +i(x²+y²) = x -iy

-2xy = x and x²+y² = -y

y =-1/2 and x = 1/2 or -1/2

or

x =0 and y² = -y but in this case y = complex number

so z = (1/2 -i/2) or (-1/2 -i/2)

|z| =[(1/2)²+(1/2)²]^1/2 = [1/4+1/4]^1/2 = 0.707