Properties of complex number
1. \[\overline{z_1+z_2+z_3+......z_n}=\overline{z_1}+\overline{z_2}+\overline{z_3}+.......+\overline{z_n}\] conjugate of sum of n complex numbers is equal to sum of conjugate of individual complex number
2.\[ \overline{\overline{z_1+z_2}}=z_1+z_2\] conjugate of conjugate of a complex number is complex number itself
3.\[ \overline{\overline{\overline{z_1+z_2}}}=\overline{z_1+z_2}\] .if conjugate is taken even number of times then we get conjugate of that complex number.
Conjugate of reciprocal of a complex number
let z=\[ \frac{1}{1+i}\]
it should be rationalised first then conjugate is found out.
\[ \frac{1}{(1+i)(1-i)}(1-i)\]
=\[ \frac{1-i}{2}\]
then conjugate is given by \[\frac{1}{2}+\frac{i}{2}\]
