z1 = 1 + 3i and z2= 2 - i and z3 = 5 + i investigate if [z2 - z3]=[z1 + z2] please explain?

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Answer 1 · 2018-03-06T09:40:20

see below

for complex numbers addition subtraction are defined as follows

#(a+ib)+-(c+id)=(a+-c)+i(b+-d)#

that is you add or subtract the real and imaginary parts separately

#z_1=1+3i;" " z_2=2-i;" "z_3=5+i#

#z_2-z_3=(2-i)-(5+i)#

#z_2-z_3=(2-5)+i(-1-1)=color(red)(-3-2i---(1))#

#z_1+z_2=(1+3i)+(2-i)#

#z_1+z_2=(1+2)+i(3-1)=color(red)(3+2i---(2))#

comparing #(1) "& "(2)# we see that

#z_2-z_3!=z_1+z_2#