# How do you simplify 5/(1+i)?

Nov 11, 2016

THe answer is $= \frac{5}{2} \left(1 - i\right)$
If a complex number is $z = a + i b$ the the conjugate is $\overline{z} = a - i b$
Then $z \cdot \overline{z} = \left(a + i b\right) \left(a - i b\right) = {a}^{2} - {i}^{2} {b}^{2} = {a}^{2} + {b}^{2}$ as ${i}^{2} = - 1$
sSo here, $\frac{5}{1 + i} = \frac{5 \left(1 - i\right)}{\left(1 + i\right) \left(1 - i\right)} = \frac{5 \left(1 - i\right)}{1 + 1} = \frac{5}{2} \left(1 - i\right)$