If Z₁=2+i and Z₂=3-4 i and Z₁ Z₁ =a+b i , then the value of -7 a+b is (where i= -1 and a , b R )

Step-by-step solution

aligned & Z ₁=2+ i Z ₂=3-4 i & Z₁ =2- i Z₂ =3+4 i & Z₁ Z₂ = 2- i 3+4 i & = (2-i)(3-4 i) (3+4 i)(3-4 i) & = 6-8 i-3 i+4 i^2 (3)^2-(4 i)^2 & = 6-1 li -4 9+16 [ i ^2=-1 ] & a + bi = 2-1 li 25 & a= 2 25 , b= -11 25 & aligned aligned & Now -7 a + b & =-7 ( 2 25 )- 11 25 & = -14-11 25 & = -25 25 =-1 aligned