Answer :
Using the square formula, the value of (1+i)^4 is -4.
The square formula is the algebraic identity which is used to find the square or difference of the sum of two terms. The square of sum of the two terms and can be calculated by multiplying the binomial by itself. The general form of square formula to find the square of the sum of two terms is given by: (a + b)^2 = a^2 + 2ab + b^2 where a and b are variables.
The given expression can be rewritten as binomial with exponent:
((1 + i)^2)^2
Using the square formula to find the square of the sum of two terms to the (1 + i)^2. Hence,
(1 + i)^2 = 1 + 2i + i^2
As 'i' iota is the square root of negative 1, i^2 = -1
1 + 2i -1 = 2i
Therefore,
(2i)^2 = 4i^2 = 4*-1 = -4
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