Question: what is the answer to 9+2i/4-3i. write in standard form, a+bi.
You "regularise" an expression such as this by changing the denominator from complex to real.
The denominator is of the form, x + iy.
So multiply by x - iy to give (x + iy)(x - iy) = x^2 - (iy)^2 = x^2 + y^2 -- a real term.
So as not to change the value of the expresion, multiply both top and bottom by the same term.
Our denomiator is (4 - 3i).
Multiply top and bottom by (4 + 3i)
The numerator becomes (9 + 2i)(4 + 3i) = 36 + 35i + 6(i^2) = 30 + 35i
The denominator becomes (4 - 3i)(4 + 3i) = 16 - 9(i^2) = 16 + 9 = 25
The expression is now: (30 + 35i)/(25) = 6/5 + i(7/5)
Answer: 6/5 + i(7/5)