( 3 +i)^7+( 3 -i)^7 is equal to

Step-by-step solution

( 3 +i)^7+( 3 -i)^7 Let 3 +i=zz=( 3 +i)=r( +i ) Then, r = 3 (i) r =1 (ii) Eq. (i) + Eq. (ii), we get r^2 ( ^2 + ^2 )=3+1 r^2=4 r=2 Eq. (ii) Eq. (i), we get = 1 3 = 6 = 6 Then, z=( 3 +i)=2 ( 6 +i 6 ) z =( 3 -i)=2 ( 6 -i 6 ) Then, ( 3 +i)^7+( 3 -i)^7= [2 6 +i 6 ]^7+ [2 6 -i 6 ]^7=2^7 7 6 +i 7 6 +2^7 7 6 -i 7 6 (By De-moiver theorem) =2^7 7 6 +i 7 6 + 7 6 -i 7 6 =2^7 2 7 6 =2^8 ( + / 6)=-2^8 6 =-2^8 3 2 =-2^7 3 =-128 3 OBJECT END]