Given, z_{1} = 2 – i, z_{2} = 1 + i

\( | \dfrac{z_1+z_2+1}{z_1-z_2+1}|\)

\( | \dfrac{(2-i)+(1+i)+1}{(2-i)-(1+i)+1}|\)

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

= \( | \dfrac{4}{2(1-i)}|\)

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

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

= \( | \dfrac{2(1+i)}{1+1}|\)

= \( | \dfrac{2(1+i)}{2}|\)

= \( |1+i|=\sqrt{1^2+1^2}\)

\( =\sqrt{2}\)

Answered by Abhisek | 1 year agoShow that 1 + i^{10} + i^{20} + i^{30} is a real number?

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