Answer:

Step-by-step explanation:
Given


Required
Write the equation of the function 
Express the function as:

In: 

--- (1)
In 

--- (2)
Divide (2) by (1)






Substitute 5/6 for b in (1)






The function: 

Answer:
Step-by-step explanation:
a
If you expand out the brackets you get this,
(4+5i)(a+2i) = 4a + (5a)i + 8i - 10
The -10 comes from 5i * 2i.
Squaring i becomes -1.
Let's group the real stuff together,
and imaginary separately,
(4a - 10) + (5a + 8)i
For this to be purely imaginary,
the real part needs to be zero.
Therefore 4a - 10 = 0
Solve for a.
I hope it helps you get it right