Question

Could someone help me with the solving steps to this equation? please thanks

Answer 1

Explanation:

You have to rationalize the denominator by multiplying by a unit multiplier of the conjugate of it which is 1+5i:

`(-3+5i)/(1-5i)*(1+5i)/(1+5i)` You will FOIL the top and the bottom to get

`(-3-15i+5i+25i^2)/(1+5i-5i-25i^2)`. Combine like terms to get

`(-3-10i+25i^2)/(1-25i^2)`. Remember that i-squared = -1, so this simplification then becomes:

`(-3-10i+25(-1))/(1-25(-1))` which simplifies a bit more to

`(-3-10i-25)/(1+25)=(-28-10i)/(26)` but we need to make sure we can match our answer to one of the ones given, so we'll split up that numerator over the denominator to get:

`-(28)/(26)-(10i)/(26)` which then goes down to

`-1(1)/(13)-(5i)/(13)` which is choice a.