Question

properties of complex numbers ?​

Answer 1

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ListenProperties of Complex Numbers

Properties of Complex NumbersIf x, y are real and x + iy = 0 then x = 0, y = 0.

Properties of Complex NumbersIf x, y are real and x + iy = 0 then x = 0, y = 0.If x, y, p, q are real and x + iy = p + iq then x = p and y = q.

Properties of Complex NumbersIf x, y are real and x + iy = 0 then x = 0, y = 0.If x, y, p, q are real and x + iy = p + iq then x = p and y = q.Like real numbers, the set of complex numbers also satisfies the commutative, associative and distributive laws i.e., if z1, z2 and z3 be three complex numbers then,

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Answer 2

Explanation:

The law of commutativity: a + b = b + a; ab = ba, for all a, b ∈ R.

II The law of associativity: (a + b) + c =

a + (b + c); (ab)c = a(bc), for all a, b, c ∈ R.

III The law of distributivity: (a + b)c = ac + bc, for all a, b, c ∈ R.

IV The law of identity: a + 0 = a; a1 = a, for all a ∈ R.

V The law of additive inverse: Given any a ∈ R, there exists a unique x ∈ R such that

a + x = 0.

VI The law of multiplicative inverse: Given a ∈ R, a 6= 0, there exists a unique x ∈ R

such that ax = 1.

Furthermore, there is a total ordering ‘<’ on R, compatible with the above arith-

metic operations, which makes R into an ordered field. Recall that < is a total ordering

means that:

VII given any two real numbers a, b, either a = b or a < b or b < a.

The ordering < is compatible with the arithmetic operations means the fo