Question

How do you simplify `1/(6-3i)`?

Answer 1

`1/(6-3i)=(2+i)/15`

Explanation:

Multiply both the numerator and denominator by the complex conjugate of the denominator:
`color(white)("XXX")1/(6-3i)xx(6+3i)/(6+3i)`

`color(white)("XXX")=(6+3i)/(6^2-3^2i^2)`

`color(white)("XXX")=(6+3i)/(36-(9)(-1))`

`color(white)("XXX")=(6+3i)/45`

`color(white)("XXX")=(2+i)/15`