Question

Prove that 1+i÷1-i+1-i÷1+i=0

Answer 1

Step-by-step explanation:

$\frac{1 + i}{1 - i} + \frac{1 - i}{1 + i} \\ \\ = \frac{ {(1 + i)}^{2} }{1 ^{2} - {i}^{2} } + \frac{ {(1 - i)}^{2} }{ {1}^{2} - {i}^{2} } \\ \\ = \frac{1 + {i}^{2} + 2i }{1 - ( - 1)} + \frac{1^{2} + {i}^{2} - 2i }{1 - ( - 1)} \\ \\ = \frac{1 - 1 + 2i}{2} + \frac{1 - 1 - 2i}{2} \\ \\ = \frac{2i}{2} + \frac{ - 2i}{2} \\ \\ = i - i \\ \\ = 0$