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Question

How do you calculate 1+i1-i?


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Solution

Calculate the given expression:

Given expression: 1+i1-i.

Rationalize the denominator by multiplying both numerator and denominator by 1+i.

1+i1-i=1+i1+i1-i1+i1+i1-i=1+i212-i21+i1-i=12+21i+i21-i21+i1-i=1+2i+i21-i2

It is known that, i=-1, so i2=-1.

Thus,

1+i1-i=1+2i-11--1

1+i1-i=2i1+11+i1-i=2i21+i1-i=i

Therefore, 1+i1-i=i.


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