Question

Simplify 1/4-7i to get a complex number in standard a + bi form.

Answer 1

Answer:

$\frac{1}{4-7i}=\frac{4}{65}+\frac{7}{65}i$

Step-by-step explanation:

we are given

$\frac{1}{4-7i}$

Firstly, we will get rid of imaginary term from denominator

so, we will multiply conjugate to both top and bottom term

$\frac{1}{4-7i}=\frac{1\times (4+7i)}{(4-7i)\times (4+7i)}$

$\frac{1}{4-7i}=\frac{4+7i}{4^2-(7i)^2}$

$\frac{1}{4-7i}=\frac{4+7i}{16+49}$

$\frac{1}{4-7i}=\frac{4+7i}{65}$

we can also write as

so, we get

$\frac{1}{4-7i}=\frac{4}{65}+\frac{7}{65}i$