Write the complex number in standart form 6i^2-8i^3

Write the complex number in standart form 6i^2-8i^3

Question
Complex numbers
asked 2020-12-07
Write the complex number in standart form \(\displaystyle{6}{i}^{{2}}-{8}{i}^{{3}}\)

Answers (1)

2020-12-08
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
\(\displaystyle\overline{{z}}=-{6}-{8}{i}\)
0

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