Question

Square root of -1 divided by (3+8i)-(2+5i)

Answer 1

`√(-1)=i\to i^2=-1\\\\therefore\ we\ have:\\\\(i)/((3+8i)-(2+5i))=(i)/(3+8i-2-5i)=(i)/(1+3i)\\\\=(i)/(1+3i)\cdot(1-3i)/(1-3i)=(i(1-3i))/(1^2-(3i)^2)=(i-3i^2)/(1-9i^2)=(i-3(-1))/(1-9(-1))\\\\=(i+3)/(1+9)=(3+i)/(10)=0.3+0.1i`

Used:
`(a+b)(a-b)=a^2-b^2`