i cant understnad why they put absolute value sign there

why they put the complement sign above some coefficient

$\displaystyle <ae_1+be_2,ae_1+be_2>=$$\displaystyle \left | a \right |^2<e_1,e+1>+a\bar{b}<e_1,e_2>+b\bar{a}<e_2,e_1>+\ left | b \right |^2<e_2,e_2>\\$

i whould do it like this

$\displaystyle <ae_1+be_2,ae_1+be_2>=<ae_1,ae_1+be_2>+<be_2,ae_1+ be_2>=$$\displaystyle a^2<e_1,e_1>+ab<e_1,e_2>$ etc..