Question

(1+i)(1-i)^-1express in form of a+in and state value of a and b​

Answer 1

Given Expression,

$\huge{\sf{(1 + i)(1 - i) {}^{ - 1} }}$

Now,

$\sf{(1 + i)(1 - i) {}^{ - 1} } \\ \\ \implies \: \sf{ \frac{1 + i}{1 - i} } \\ \\ \sf{multiplying \: and \: dividing \: by \: conjugate} \\ \\ \implies \: \sf{ \frac{1 + i}{1 - i} \times \frac{1 + i}{1 + i} } \\ \\ \implies \: \sf{ \frac{(1 + i) {}^{2} }{1 {}^{2} - ( i) {}^{2} }} \\ \\ \implies \: \sf{ \frac{1 + 2i + i {}^{2} }{1 - i {}^{2} } } \\ \\ \sf{since \: i {}^{2} = - 1} \\ \\ \implies \: \sf{ \frac{2i}{2} } \implies \: \sf{i} \\ \\ \implies \: \underline{ \boxed{ \sf{0 + i}}}$

Here,

a=0 and b=1