Question:
Find the modulus of(1+i)/(1-i) (1-i) /(1+i)
Answer:
Given expression is
{(1+i)/(1-i)} - {(1-i)/(1+i)}
= [{(1+i)*(1+i)}/{(1-i)*(1+i)}] - [{(1-i)*(1-i)}/{(1+i)*(1-i)}]
= {(1+i)2 /(1-i2 )} - {(1-i)2 /(1 - i2 )}
= (1 + i2 + 2i)/(1+1) - (1 + i2 - 2i)/(1+1) (since i2 = -1)
= (1 - 1 +2i)/2 - (1- 1 -2i)/2
= 2i/2 + 2i/2
= i + i
= 2i
= 0 + 2i
Now modulus = √(o + 22 ) = √4 = 2
So modulus of the expression = 2
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