Question

Q1.(1+i)(1-i) power is -1 state the value of a and b

Answer 1

Step-by-step explanation:

Answer: a = 0 , b = 1

Step-by-step explanation:

Given complex number,

$\begin{gathered}(1+i)(1-i)^{-1}\\\;\\=\dfrac{1+i}{1-i}\\\;\\\text{Multiplying by (1+i) in denominator and numerator,}\\\;\\=\dfrac{(1+i)(1+i)}{(1-i)(1+i)}\\\;\\=\dfrac{(1+i)^2}{1^2-i^2}\\\;\\=\dfrac{1^2+i^2+2i}{1-(-1)}\\\;\\=\dfrac{1-1+2i}{1+1}\\\;\\=\dfrac{2i}{2}\\\;\\=i\\\;\\=0+i\end{gathered}$

Comparing this complex number with standard form of complex number a+ib;

We have,

a = 0

b = 1

Note: 1) i = √(-1)

2) i² = -1

3) i³ = -i

4) i⁴ = 1

Answer 2

Step-by-step explanation:

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