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

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Question : 44 of 52
Marks: +1, -0
Let z1z_1 = 2 - i , z2z_2 = - 2 + i. Find
(i) Re (z1z2z1)\left(\frac{z_1 z_2}{\overline{z_1}}\right) , (ii) Im (1z1z1)\left(\frac{1}{\overline{z_1 z_1}}\right)
Solution:  
We have, z1z_1 = 2 - i , z2=2+i(i)z_2 = -2 + i \quad (i)z_1z_2$=(2i)(2+i)=4+2i+2i= (2 - i) (- 2 + i) = - 4 + 2i + 2i -i^2=4+1+4i=3+4iAlso,= - 4 + 1 + 4i = - 3 + 4i \quad \text{Also},z_1↖{-}=2+i= 2 + i \quad \therefore{z_1z_2}/z_1↖{-}=={-3+4i}/{2+i}=={-3+4i}/{2+i}×\times{2-i}/{2-i}=\quad ={-6+3i+8i+4}/{4+1}=={-2+11i}/5==-2/5 + {11}/5 i==({z_1z_2}/z_1↖{-}) Re\quad \therefore \ \text{Re}2/5== -z_1z_1↖{-}(ii)\quad (ii)1/{z_1z_1↖{-}}=(2i)(2+i)=4+1=5Now,= (2 - i) (2 + i) = 4 + 1 = 5 \quad \text{Now},1/5==1/5==(1/{z_1z_1↖{-}})$ = 0
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