TS Inter 2nd Year Maths 2A Complex Numbers Formulas

Learning these TS Inter 2nd Year Maths 2A Formulas Chapter 1 Complex Numbers will help students to solve mathematical problems quickly.

TS Inter 2nd Year Maths 2A Complex Numbers Formulas

→ A complex number is an ordered pair of real numbers. It is denoted by (a, b); a ∈ R, b ∈ R.
z = a + ib
Re(z) = a ; Im(z) = b

→ Two complex numbers z1 = a + ib and z2 = c + id are said to be equal if a = c, b = d.

→ Algebra of complex numbers
(a) z = z1 + z2 = (a + c) + i (b + d)
(b) z = z1 – z2 = (a – c) + i (b – d)
(c) z = z1/z2 = \(\frac{a c+b d}{c^2+d^2}+\frac{i(b c-a d)}{c^2+d^2}\)
(d) z = z1 . z2 = (ac – bd) + i (ad + be)

→ If z = a + ib, then conjugate of complex number is z̅ = a – ib
z . z̅ = a2 + b2

TS Inter 2nd Year Maths 2A Complex Numbers Formulas

→ If z = a + ib, then modulus of z is represented by |z| = \(\sqrt{a^2+b^2}\)

→ Any real number θ satisfy the equation x = r cos θ; y = r sin θ.

→ Arg z = tan-1\(\frac{{Im}(z)}{{Re}(z)}\) = tan-1\(\frac{y}{x}\), -π < Arg z < π
(a) Arg (z1. z2) = Arg z1 + Arg z2+ nπ for some π ∈ {-1,0,1}.
(b) Arg (z1/z2) = Arg z1 – Arg z2 + nπ, π ∈ (-1,0,1}.

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