Question

यदि $z_1 = 2 - \iota$, $z_2 = 1 + \iota$, $\left | \dfrac{z_1 + z_2 + 1}{z_1 - z_2 + 1}\right|$ का मान ज्ञात कीजिए l

Answer 1

Answer:

Step-by-step explanation:

प्रश्नानुसार  

$z_1=2-i,z_2=1+i$

अब   $z_1+z_2+1=2-i+1+i+1=4$

तथा    $z_1-z_2+i=2-i-1-i+i=1-i$

∵$|\frac{z_1}{z_2} |=\frac{|z_1|}{|z_2|}$

अतः  

$|\frac{z_1+z_2+1}{z_1-z_2+i} |=|\frac{4}{1-i} |\\\\=\frac{|4|}{|1-i|} \\\\=\frac{4}{\sqrt{(1)^{2}+(-1)^{2}} } \\\\=\frac{4}{\sqrt{1+1} } \\\\=\frac{4}{\sqrt{2} } \\\\=2\sqrt{2}$