If Z_r= ( 2^r )+i ( 2^r ) for r=1,2,3, . , then Z₁ Z₂ Z₃ equals to

Step-by-step solution

aligned & Given, z_r= ( 2^ )+i ( 2^r ) & z₁ z₂ z₃ =e^ i 2 e^ i 2^2 e^ i 2^3 & =e^ i ( 2 + 2^2 + 2^3 + ) & =e^ i ( / 2 1 ) =e^ ( ) & = +i =-1+i(0) & =-1 & aligned