show that √i+√-i is equal to√2
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Step-by-step explanation:
z=(a+bi) be a complex number which is a square root of i, that is i=z2=(a2−b2)+2abi.Equating real and imaginary parts we have,a2−b2=0,2ab=1
The two real solutions to this pair of equations are a=1√2,b=1√2 and a=−1√2,b=−1√2.
Sq root of i is =+/-(1+i)/root2
Si.ilarly can be found for - i
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