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Let
i = a + ib,
Square both sides,
I = (a+ib)^2.......3
i = a^2 + i^2b^2 + 2abi
i = a^2 - b^2 + 2abi,
Equating both sides real and imaginary value,
a^2 - b^2 = 0
a^2 = b^2.....1
2ab = 1
a = 1/2b......2
Sub 2 in 1,
You get, b=+-1/2, a=+-1/2,
From EQ 3,
i = +-1/2 + i+-1/2...ans
Thank you.
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