Help me with this imaginary number stuff.?

Question

2
8+5i

Where 'i' is an imaginary unit.

Write the quotient in the form of a+bi.

Answer 1

2 / ( 8 + 5 i )
2 ( 8 - 5 i ) / ( 8 + 5i )( 8 - 5i )
2( 8 - 5 i ) / ( 64 - 25 i ² )
2( 8 - 5 i ) / ( 64 + 25 )
2( 8 - 5 i ) / 89
(2/89) (8 - 5 i)

Answer 2

General rule: If you are dividing by a+bi, multiply
numerator and denominator by a- bi to rationalise
the denominator.
So we get
2/ (8+5i) = 2(8-5i)/89 = 16/89 -10i/89.

Answer 3

I assume it was 2/(8+5i) and if so, multiply the top and bottom
by 8-5i.