Question

Explain how adding and subtracting complex numbers is like adding and subtracting algebraic expressions

Answer 1

suppose there are two complex numbers
say (a+ib) and (c+id)
now, you have to add the two complex numbers. the result will obviously be an another complex number. what would you do?
then, you would add the real terms 'a' and 'c' of the complex numbers (a+ib) and (c+id) respectively and add the imaginary parts of the two as well (i.e. 'b' and 'd'). therefore, the answer that we will get after adding the two complex numbers is (a+c)+i(b+d)
for example, if a=5, b=3, c=4 and d=2, then the addition of the two complex numbers (5+3i) and (4+2i) is (9+5i)
i.e. real parts and the imaginary parts get added separately...
similarly, the subtraction of two complex numbers goes like this...