# Perform indicated operation (simplify as a+bi)

• April 12th 2009, 04:07 PM
Hapa
Perform indicated operation (simplify as a+bi)
1 + 4i / 1 - i

• April 12th 2009, 04:23 PM
mr fantastic
Quote:

Originally Posted by Hapa
1 + 4i / 1 - i

Is it (1 + 4i)/(1 - i), that is, $\frac{1 + 4i}{1 - i} ?$ Please be less ambiguous when you post.
• April 12th 2009, 04:26 PM
Hapa
My apologies. Yes, it is as you listed

(1 + 4i) / (1 - i)
• April 12th 2009, 04:28 PM
e^(i*pi)
Quote:

Originally Posted by Hapa
My apologies. Yes, it is as you listed

(1 + 4i) / (1 - i)

Use the difference of two squares $a^2-b^2 = (a-b)(a+b)$
and $i^2 = -1$ to rationalise the denominator

Spoiler:
$\frac{1+4i}{1-i} \times \frac{1+i}{1+i} = \frac{(1+4i)(1+i)}{(1-i)(1+i)}$

$\frac{1+i+4i+4i^2}{1-(i^2)} = \frac{-3+5i}{2} = -1.5+2.5i$