If z₁=1-2 i ; z₂=1+i and z₃=3+4 i , then ( 1 z₁ + 3 z₂ ) z₃ z₂ =

Step-by-step solution

We have, aligned & z₁=1-2 i, z₂=1+i, & z₃=3+4 i aligned Now, ( 1 z₁ + 3 z₂ ) z₃ z₂ = ( 1 1-2 i + 3 1+i ) ( 3+4 i 1+i ) aligned & = (1+i)+3(1-2 i) (1-2 i)(1+i) 3+4 i 1+i = 4-5 i 3-i 3+4 i 1+i & = 12+16 i-15 i+20 3+3 i-i+1 = 32+i 4+2 i & = (32+i)(2-i) 2(2+i)(2-i) = 64+2 i-32 i+1 2(4+1) & = 65-30 i 10 = 13 2 -3 i aligned