{"id":574,"date":"2020-11-13T06:00:10","date_gmt":"2020-11-13T00:30:10","guid":{"rendered":"http:\/\/physicscatalyst.com\/article\/?p=574"},"modified":"2024-07-28T04:28:33","modified_gmt":"2024-07-27T22:58:33","slug":"complex-numbers-formulas","status":"publish","type":"post","link":"https:\/\/physicscatalyst.com\/article\/complex-numbers-formulas\/","title":{"rendered":"Complex Numbers Formulas for Class 11 Maths"},"content":{"rendered":"\n
\"Complex<\/figure>\n\n\n\n

Complex Numbers is an important topic. Here are list of Complex Numbers Formulas<\/p>\n\n\n\n

Complex Numbers<\/h2>\n\n\n\n

Complex numbers are defined as an ordered pair of real numbers like (x,y) where<\/p>\n\n\n\n

$z=(x,y)=x+iy$ and $i = \\sqrt {-1}$<\/p>\n\n\n\n

and both x and y are real numbers and x is known as real part of complex number and y is known as imaginary part of the complex number.<\/p>\n\n\n\n

Addition of complex numbers<\/h2>\n\n\n\n

Let z1<\/sub>=x1<\/sub>+iy1<\/sub> and z2<\/sub>=x2<\/sub>+iy2<\/sub> then<\/p>\n\n\n\n

z1<\/sub>+z2<\/sub>=(x1<\/sub>+x2<\/sub>)+i(y1<\/sub>+y2<\/sub>)<\/p>\n\n\n\n

Subtraction<\/h2>\n\n\n\n

z1<\/sub>-z2<\/sub>=(x1<\/sub>-x2<\/sub>)+i(y1<\/sub>-y2<\/sub>)<\/p>\n\n\n\n

Multiplication<\/h2>\n\n\n\n

(z1<\/sub>.z2<\/sub>)=(x1<\/sub>+iy1<\/sub>).(x2<\/sub>+iy2<\/sub>)<\/p>\n\n\n\n

Multiplicative Inverse<\/h2>\n\n\n\n

for $z=a+ib$<\/p>\n\n\n\n

z-1<\/sup> is given by<\/p>\n\n\n\n

=$(\\frac{a}{a^{2}+b^{2}})+i(\\frac{-b}{a^{2}+b^{2}})$<\/p>\n\n\n\n

Complex conjugate <\/h2>\n\n\n\n

$z=x+iy$ Then complex conjugate is given by<\/p>\n\n\n\n

 $\\bar{z}=x-iy$<\/p>\n\n\n\n

Properties of Complex Conjugate<\/span><\/p>\n\n\n\n