Question

How do you divide `7/(4i)`?

Answer 1

`7/(4i)=-7/4i`

Explanation:

In complex numbers, when we have to divide a number by a complex number, say `a+bi`, we do it by multiplying numerator and denominator by its complex conjugate, which for `a+bi` is `a-bi`

Observe that we only change the sign of imaginary part, but not that of real part.

Here we have to find `7/(4i)`, i.e. divide `7` by `4i` or `0+4i`.

As complex conjugate of `0+4i` is `0-4i` i.e. `-4i`, we multiply numerator and denominator by `-4i`

Hence, `7/(4i)=(7xx(-4i))/(4ixx(-4i))`

= `(-28i)/(-16i^2)`

but in complex numbers `i^2=-1`

Hence, `7/(4i)=(-28i)/(-16i^2)=(-28i)/16=(-7i)/4=-7/4i`