InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
Define addition of two complex numbers. |
|
Answer» Let z1= a + ib and z2 = c + id be any two complex numbers. Then addition of z1 and z2 defined as z1 + z2 = (a + c) + i(b + d) which is again a complex number. Properties of addition of complex numbers: (i) Closure property: The sum of two complex numbers is always a complex number, i.e., addition is closed in C set of complex numbers. (ii) Commutative property: For any two complex numbers z1 and z2 we have z1 + z2 = z2 + z1 (iii) Associative properly: For any complex numbers z1, z2 and Z3, we have z1 + (z2 + z3) = (z1 + z2) + z3 (iv) Existence of additive identity: For any complex number z, we have z + 0 = 0 +-z = z Thus, 0 is the additive identity for complex numbers. (v) Existence of additive inverse: Every complex number z-a + ib has -z = (-a) + i(-b) as its additive inverse, as z + (-z) = (-z) + z = 0. |
|