give an example to show that subtraction of complex no. is not commutative

Question

sum of class 11ths companion mathematics

Answer 1

No subtraction is commutative, that is, a-b≠b-a, unless they are equal.

Let two complex numbers be z₁=A+iB and z₂=C+iD, then z₁-z₂=A-C+i(B-D), and z₂-z₁=C-A+i(D-B).

Comparing real and imaginary parts:

A-C≠C-A and B-D≠D-B, so subtraction is not commutative for complex numbers, unless they are equal.