Find the modulus of {1+i}{1-i}-{1-i}{1+i}

Question

Find the modulus of \( \dfrac{1+i}{1-i}-\dfrac{1-i}{1+i}\)

Asked by Abhisek | 1 year ago | 113

0 0

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Accepted Answer

\( \dfrac{1+i}{1-i}-\dfrac{1-i}{1+i}\)

= \( \dfrac{(1+i)^2-(1-i)^2}{(1-i)(1+i)}\)

= \( \dfrac{1+i^2+2i-1-i^2+2i}{1^2+1^2}\)

= \( \dfrac{4i}{2}=2i\)

\( \dfrac{1+i}{1-i}-\dfrac{1-i}{1+i}\)

= \( |2i|\)

=\( \sqrt{2^2}=2\)

Answered by Pragya Singh | 1 year ago