Answer :

Given: Re(z2) = 0 and |z| = 2

Let z = x + iy



[given]


Squaring both the sides, we get


x2 + y2 = 4 …(i)


Since, z = x + iy


z2 = (x + iy)2


z2 = x2 + i2y2 + 2ixy


z2 = x2 + (-1)y2 + 2ixy


z2 = x2 – y2 + 2ixy


It is given that Re(z2) = 0


x2 – y2 = 0 …(ii)


Adding eq. (i) and (ii), we get


x2 + y2 + x2 – y2 = 4 + 0


2x2 = 4


x2 = 2


x = ±√2


Putting the value of x2 = 2 in eq. (i), we get


2 + y2 = 4


y2 = 2


y = ±√2


Hence, z = √2 ± i√2, -√2 ± i√2


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