Question

Plzz... solve it it's very urgent

Answer 1

if $z$ is a complex number then, $\bar{z}$ is known conjugate of complex, $z$.

where, if $z=a+\iota b$, where a is real part and b is imaginary part of $z$

then, $\bar{z}=a-\iota b$

now, mode of $z$ = $|z|$ = $\sqrt{a^2+b^2}$

and mode of $\bar{z}$ = $|\bar{z}|$ = $\sqrt{a^2+(-b)^2}$

= $\sqrt{a^2+b^2}$

here it is clear that, $|z|=|\bar{z}|=\sqrt{a^2+b^2}$

e.g., $|z|=|\bar{z}|$ hence proved