The modulus of the following complex number 1+i 1-i - 1-i 1+i is

Step-by-step solution

Let z = 1+i 1-i - 1-i 1+i . Simplify the first term by multiplying the numerator and denominator by the conjugate of the denominator (1+i) : 1+i 1-i = (1+i)(1+i) (1-i)(1+i) = 1 + 2i + i^2 1^2 - i^2 = 1 + 2i - 1 1 + 1 = 2i 2 = i . Simplify the second term by multiplying the numerator and denominator by the conjugate of the denominator (1-i) : 1-i 1+i = (1-i)(1-i) (1+i)(1-i) = 1 - 2i + i^2 1^2 - i^2 = 1 - 2i - 1 1 + 1 = -2i 2 = -i . Substitute these values back into the expression for z : z = i - (-i) = i + i = 2i .