Answer:
[tex]\frac{4}{29}-\frac{10i}{29}[/tex]
Step-by-step explanation:
2 divided by the quantity of 2 plus 5i
[tex]\frac{2}{2+5i}[/tex]
to divide we mutliply the fraction by the conjugate of denomiator
conjugate of 2+5i is 2-5i
[tex]\frac{2}{2+5i}*\frac{2-5i}{2-5i}[/tex]
(2+5i)(2-5i)= 4 +10i +10i - 25i^2
the value of i^2=-1
(2+5i)(2-5i)= 4 +10i +10i - 25i^2= 4 - 25(-1)= 29
[tex]\frac{4-10i}{29}[/tex]
[tex]\frac{4}{29}-\frac{10i}{29}[/tex]
