A complex number z is of the form x+iy (standard form) , where x and y are real numbers (called the real and imaginary parts of z). The manipulation with complex numbers follow the same rules as for real numbers , except that the symbol i satisfies \(\displaystyle{i}^{{2}}=-{1}\). (i is square root of -1).

The simplification of the given expression:

\(\displaystyle{i}^{{2}}=-{1}^{{3}}\)

\(\displaystyle{z}={6}{i}^{{2}}-{8}{i}\)

\(\displaystyle={6}\cdot{\left(-{1}\right)}-{8}{i}^{{i}}\)

=-6-8*(-1)i

Given the complex number z=x+iy (with x an d y both real), its complex conjugate z(bar) (see above) is defined to be the complex number x-iy.

z=x+iy (x,y real)

the complex conjugate

\(\displaystyle\overline{{z}}={x}-{i}{y}\)

Given

z=-6+8i

Therefore, its complex conjugate is

\(\displaystyle\overline{{z}}=-{6}-{8}{i}\)

The simplification of the given expression:

\(\displaystyle{i}^{{2}}=-{1}^{{3}}\)

\(\displaystyle{z}={6}{i}^{{2}}-{8}{i}\)

\(\displaystyle={6}\cdot{\left(-{1}\right)}-{8}{i}^{{i}}\)

=-6-8*(-1)i

Given the complex number z=x+iy (with x an d y both real), its complex conjugate z(bar) (see above) is defined to be the complex number x-iy.

z=x+iy (x,y real)

the complex conjugate

\(\displaystyle\overline{{z}}={x}-{i}{y}\)

Given

z=-6+8i

Therefore, its complex conjugate is

\(\displaystyle\overline{{z}}=-{6}-{8}{i}\)