{"id":36255,"date":"2022-11-28T10:13:37","date_gmt":"2022-11-28T04:43:37","guid":{"rendered":"https:\/\/tsboardsolutions.com\/?p=36255"},"modified":"2022-11-28T10:13:37","modified_gmt":"2022-11-28T04:43:37","slug":"ts-inter-2nd-year-maths-2a-complex-numbers-formulas","status":"publish","type":"post","link":"https:\/\/tsboardsolutions.com\/ts-inter-2nd-year-maths-2a-complex-numbers-formulas\/","title":{"rendered":"TS Inter 2nd Year Maths 2A Complex Numbers Formulas"},"content":{"rendered":"
Learning these TS Inter 2nd Year Maths 2A Formulas<\/a> Chapter 1 Complex Numbers will help students to solve mathematical problems quickly.<\/p>\n \u2192 A complex number is an ordered pair of real numbers. It is denoted by (a, b); a \u2208 R, b \u2208 R. \u2192 Two complex numbers z1<\/sub> = a + ib and z2<\/sub> = c + id are said to be equal if a = c, b = d.<\/p>\n \u2192 Algebra of complex numbers \u2192 If z = a + ib, then conjugate of complex number is z\u0305 = a – ib <\/p>\n \u2192 If z = a + ib, then modulus of z is represented by |z| = \\(\\sqrt{a^2+b^2}\\)<\/p>\n \u2192 Any real number \u03b8 satisfy the equation x = r cos \u03b8; y = r sin \u03b8.<\/p>\n \u2192 Arg z = tan-1<\/sup>\\(\\frac{{Im}(z)}{{Re}(z)}\\) = tan-1<\/sup>\\(\\frac{y}{x}\\), -\u03c0 < Arg z < \u03c0 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 \u2192 A complex number is an ordered pair of real numbers. It is denoted by (a, b); a \u2208 R, b \u2208 R. z = … Read more<\/a><\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[26],"tags":[],"yoast_head":"\nTS Inter 2nd Year Maths 2A Complex Numbers Formulas<\/h2>\n
\nz = a + ib
\nRe(z) = a ; Im(z) = b<\/p>\n
\n(a) z = z1<\/sub> + z2<\/sub> = (a + c) + i (b + d)
\n(b) z = z1<\/sub> – z2<\/sub> = (a – c) + i (b – d)
\n(c) z = z1<\/sub>\/z2<\/sub> = \\(\\frac{a c+b d}{c^2+d^2}+\\frac{i(b c-a d)}{c^2+d^2}\\)
\n(d) z = z1<\/sub> . z2<\/sub> = (ac – bd) + i (ad + be)<\/p>\n
\nz . z\u0305 = a2<\/sup> + b2<\/sup><\/p>\n
\n(a) Arg (z1<\/sub>. z2<\/sub>) = Arg z1<\/sub> + Arg z2<\/sub>+ n\u03c0 for some \u03c0 \u2208 {-1,0,1}.
\n(b) Arg (z1<\/sub>\/z2<\/sub>) = Arg z1<\/sub> – Arg z2<\/sub> + n\u03c0, \u03c0 \u2208 (-1,0,1}.<\/p>\n","protected":false},"excerpt":{"rendered":"