multiply with conjugate
[tex] \frac{1}{6 + 5i} \times \frac{6 - 5i}{6 - 5i} = \frac{6 - 5i}{36 + 25} \\ = \frac{6}{61} - \frac{5}{61} i[/tex]
Answer:
The required form is [tex]\frac{6}{61}-\frac{5i}{61}[/tex] or [tex]\frac{6}{61}+\frac{-5i}{61}[/tex]
Step-by-step explanation:
Consider the provided complex number.
[tex]\frac{1}{(6+5i)}[/tex]
Multiply the denominator and numerator with the conjugate of the denominator.
[tex]\frac{1}{(6+5i)}\times \frac{6-5i}{6-5i}[/tex]
[tex]\frac{6-5i}{(6)^2-(5i)^2}[/tex]
[tex]\frac{6-5i}{36+25}[/tex]
[tex]\frac{6-5i}{61}[/tex]
[tex]\frac{6}{61}-\frac{5i}{61}[/tex] or [tex]\frac{6}{61}+\frac{-5i}{61}[/tex]
Hence, the required form is [tex]\frac{6}{61}-\frac{5i}{61}[/tex] or [tex]\frac{6}{61}+\frac{-5i}{61}[/tex]
