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

1 Answer
Sep 5, 2017

Answer:

#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#