If z1 = 2 – i, z2 = 1 + i, find $$| \dfrac{z_1+z_2+1}{z_1-z_2+1}|$$

Asked by Pragya Singh | 1 year ago |  65

##### Solution :-

Given, z1 = 2 – i, z2 = 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 ago

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