Question

Answer 10 please
Urgent hai ​

Answer 1

Given :-

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$\tt\longrightarrow{z_1 = 2 - i}$

$\tt\longrightarrow{z_2 = 1 + i}$

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Solution :-

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$\rm\implies{\bigg| \dfrac{z_1 + z_2 + 1}{z_1 - z_2 + 1} \bigg|}$

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Putting the values

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$\rm\implies{\bigg| \dfrac{(2 - i) + (1 + i) + 1}{(2 - i) - (1 + i) + 1} \bigg|}$

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$\rm\implies{\bigg| \dfrac{2 - i + 1 + i + 1}{2 - i - 1 - i + 1} \bigg|}$

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$\rm\implies{\bigg| \dfrac{4}{2 - 2i} \bigg|}$

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$\rm\implies{\bigg| \dfrac{2}{1 - i} \bigg|}$

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Rationalising the denominator

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$\rm\implies{\bigg| \dfrac{2}{1 - i} \times \dfrac{1 + i}{1 + i} \bigg|}$

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$\rm\implies{\bigg| \dfrac{2(1 + i)}{(1 - i)(1 + i)} \bigg|}$

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$\rm\implies{\bigg| \dfrac{2 + 2i}{1 - i^2} \bigg|}$

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$\: \: \: \: \: \: \: \: \star\bf\: \: \: {i^2 = -1}$

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$\rm\implies{\bigg| \dfrac{2 + 2i}{1 + 1} \bigg|}$

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$\rm\implies{\bigg| \dfrac{2 + 2i}{2} \bigg|}$

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$\rm\implies{| 1 + 1i |}$

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☆ Modulus

$\: \: \: \: \: \: \: \: \star\bf\: \: \: {| x + iy | = \sqrt{x^2 + y^2}}$

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$\rm\implies{\sqrt{(1)^2 + (1)^2}}$

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$\rm\implies{\sqrt{1 + 1}}$

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$\rm\implies{\sqrt{2}}$

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Hence,

• The required answer is $\bf{\sqrt{2}}$