Answer:
[tex]\frac{1}{4-7i}=\frac{4}{65}+\frac{7}{65}i[/tex]
Step-by-step explanation:
we are given
[tex]\frac{1}{4-7i}[/tex]
Firstly, we will get rid of imaginary term from denominator
so, we will multiply conjugate to both top and bottom term
[tex]\frac{1}{4-7i}=\frac{1\times (4+7i)}{(4-7i)\times (4+7i)}[/tex]
[tex]\frac{1}{4-7i}=\frac{4+7i}{4^2-(7i)^2}[/tex]
[tex]\frac{1}{4-7i}=\frac{4+7i}{16+49}[/tex]
[tex]\frac{1}{4-7i}=\frac{4+7i}{65}[/tex]
we can also write as
so, we get
[tex]\frac{1}{4-7i}=\frac{4}{65}+\frac{7}{65}i[/tex]
