Question

Simplify 1/(6+5i) to get a complex number in standard a + bi form

Answer 1

Answer:

The required form is $\frac{6}{61}-\frac{5i}{61}$ or $\frac{6}{61}+\frac{-5i}{61}$

Step-by-step explanation:

Consider the provided complex number.

$\frac{1}{(6+5i)}$

Multiply the denominator and numerator with the conjugate of the denominator.

$\frac{1}{(6+5i)}\times \frac{6-5i}{6-5i}$

$\frac{6-5i}{(6)^2-(5i)^2}$

$\frac{6-5i}{36+25}$

$\frac{6-5i}{61}$

$\frac{6}{61}-\frac{5i}{61}$ or $\frac{6}{61}+\frac{-5i}{61}$

Hence, the required form is $\frac{6}{61}-\frac{5i}{61}$ or $\frac{6}{61}+\frac{-5i}{61}$

Answer 2

multiply with conjugate

$\frac{1}{6 + 5i} \times \frac{6 - 5i}{6 - 5i} = \frac{6 - 5i}{36 + 25} \\ = \frac{6}{61} - \frac{5}{61} i$