Find the modulus of 1+i/1-i

Dear student

Let z = \frac{1 + i}{1 - i} . Then z = \frac{1 + i}{1 - i} \times \frac{1 + i}{1 + i} = \frac{{(1 + i)}^{2}}{1 - i^{2}} = \frac{1 + 2 i + i^{2}}{1 + 1} = i = 0 + i ∴ |z| = \sqrt{0^{2} + 1^{2}} = 1

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