Express the following complex numbers in the standard form a + ib : \

1.	Express the following complex numbers in the standard form a + ib : \(\frac{1-i}{1+i}\)
Answer» Given: ⇒ a + ib = \(\frac{1-i}{1+i}\) Multiplying and dividing by 1-i ⇒ a + ib = \(\frac{1-i}{1+i}\) x \(\frac{1-i}{1-i}\) ⇒ a + ib = \(\frac{1^2+i^2-2(1)(i)}{1^2-(i)^2}\) We know that i²= -1 ⇒ a + ib = \(\frac{1+(-1)-2i}{1-(-1)}\) ⇒ a + ib = \(\frac{-2i}{2}\) ⇒ a + ib = -i ⇒ a + ib = 0 - i ∴ The values of a, b is 0, -1.

Express the following complex numbers in the standard form a + ib : \(\frac{1-i}{1+i}\)

Answer»

Given:

⇒ a + ib = \(\frac{1-i}{1+i}\)

Multiplying and dividing by 1-i

⇒ a + ib = \(\frac{1-i}{1+i}\) x \(\frac{1-i}{1-i}\)

⇒ a + ib = \(\frac{1^2+i^2-2(1)(i)}{1^2-(i)^2}\)

We know that i²= -1

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

⇒ a + ib = \(\frac{-2i}{2}\)

⇒ a + ib = -i

⇒ a + ib = 0 - i

∴ The values of a, b is 0, -1.