Calculate: ( 2+i√(5) )( √(5)-i).

[Brief intro to question] This is a typical example of A-Levels Further maths exam question. The aim of it is to obtain a single number (it can be both - either just real with no imaginary values i or complex with i values). To solve questions like these it is the most important to remember definition of imaginary number i within a complex number; thereafter with knowledge of that it becomes single algebra where you need to simplify the equation above by just opening the brackets.Imaginary number i is defined with the equation x²=-1, or in other words i=√(-1). With knowledge of this you can prove that, for example, i²=-1 etc. Now, this questions asks you to calculate outcome of the equation above; it can also be understood as to simplify the equation to as few numbers as possible. In this case, all you have to do is open the brackets, which can be done by just multiplying the each member of first brackets with the two member of other brackets individually, then summing those together to get an expression.2√(5)-2i+5i-i²√(5).Now, let's simplify this to: 2√(5)+3i-i²√(5). If you remember from definition above, i=√(-1), therefore, i²=-1Putting this into to simplified equation yields: 2√(5)+3i-(-1)√(5). This can be further simplified to 3√(5)+3i, which is the final answer as there are no further simplifications available.