Question

What is 2 divided by the quantity of 2 plus 5i simplified

Answer 1

This is simple to me, I am a math wiz, it is the quantity of 4 minus 10i divided by 29

Answer 2

`(4)/(29)-(10i)/(29)`

Explanation:

2 divided by the quantity of 2 plus 5i

`(2)/(2+5i)`

to divide we mutliply the fraction by the conjugate of denomiator

conjugate of 2+5i is 2-5i

`(2)/(2+5i)*(2-5i)/(2-5i)`

(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

`(4-10i)/(29)`

`(4)/(29)-(10i)/(29)`