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NCERT Class XI Mathematics - Complex Numbers and Quadratic Equations - Solutions

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Question : 42 of 52
Marks: +1, -0
If z1z_1 = - i , z2z_2 = + i , find ∣z1+z2+1z1−z2+1∣\left| \frac{z_1+z_2+1}{z_1-z_2+1} \right|
Solution:  
We have, z1z_1 = 2 – i, z2z_2 = 1 + i, z1+z2z_1 + z_2 + 1 = (2 – i) + (1 + i) + 1 = 4 + 0i and z1−z2z_1 - z_2 + 1 = (2 – i) – (1 + i) + 1 = 2 – 2i
∴ ∣z1+z2+1z1−z2+1∣\left| \frac{z_1+z_2+1}{z_1-z_2+1} \right| = ∣z1+z2+1∣∣z1−z2+1∣\frac{\left| z_1+z_2+1 \right|}{\left| z_1-z_2+1 \right|} = ∣4∣4+4\frac{\left|4\right|}{\sqrt{4+4}} = 422\frac{4}{2\sqrt{2}} = 2\sqrt{2}
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