AP EAMCET202123 Aug 2021Evening ShiftMathematicsComplex NumberActual
If Z₁ and Z₂ are conjugate complex numbers. Match the items under the following columns? Options : array llll A & B & C & D array
Options
- Aarray llll 3 & 1 & 4 & 2 array
- Barray llll 3 & 1 & 2 & 4 array
- Carray llll 1 & 2 & 4 & 3 array
- Darray llll 2 & 4 & 3 & 1 array
Correct answer
B. array llll 3 & 1 & 2 & 4 array
Step-by-step solution
Given Z₁, Z₂ are conjugate complex numbers. Let Z₁=a+i b |Z₁ |^2= ( a^2+b^2 )^2=a^2+b^2 Z₂=a-i b (i) Z₁ Z₂=(a+i b)(a-i b)=a^2+b^2= |Z₁ |^2 (ii) Z₁+Z₂=0a+i b+a-i b=02 a=0 a=0 imaginary axis. (iii) If Z₁=a+i b aligned & Im (Z₁ )=b & Im (-Z₂ )= Im (-(a-i b)) aligned = Im (-a+i b)=b Hence, Im (Z₁ )= Im (-Z₂ ) (iv) Re (Z₁ )=a Re (Z₂ )=a Re (Z₁ )= Re (Z₂ ) A -(3) ; B -(1) ; C -(2) ; D -(4) .