​ Express each of the following in a + ib form. i) (1+i)/(1-i) ii) (2-4i)/(1-3i) iii)(3+2i)/(5+i)

Question

Express each of the following in a + ib form.

i) \(\frac{1+i}{1-i}\)

ii) \(\frac{2-4i}{1-3i}\)

iii) \(\frac{3+2i}{5+i}\)

Answer 1

(i)  \(\frac{1+i}{1-i}\) = \(\frac{1+i}{1-i}\)x\(\frac{1+i}{1-i}\) = \(\frac{(1+i)^2}{1+1}\)

= \(\frac{1+2i-1}{2} = \frac{2i}{2} = i\)