What is the standard form of the complex number ( 6 - 2i )/( 4 +14i )?

The standard form of the complex number is represented by
the rectangular form, that  is:

z = x +
i*y

The standard form does not allow for a complex numbers
to be found at the denominator.

For the beginning, we'll
factorize both, numerator and denominator, by 2:

( 6 - 2i
)/( 4 +14i ) = 2(3 - i)/2(2 + 7i)

We'll simplify and we'll
get: (3 - i)/(2 + 7i)

We'll have to get the complex
number out of the denominator. For this reason, we'll have
to multiply the numerator and denominator by the conjugate of the denominator: (2 -
7i).

(3-i)/(2+7i) = (3-i)*(2 - 7i)/(2+7i)*(2 -
7i)

(3-i)*(2 - 7i)/(2+7i)*(2 - 7i) = (6 - 21i - 2i +
7i^2)/(4 + 49), i^2 = -1

(6 - 21i - 2i - 7)/(4 + 49) = (-1
- 23i)/(53)

The standard form of the given
complex number is:

z = -1/53 -
(23/53)*i