Find the multiplicative inverse of the following complex numbers : 1 �

1.	Find the multiplicative inverse of the following complex numbers : 1 – i
Answer» Given complex number is Z=1-i We know that the multiplicative inverse of a complex number Z is Z^-1 (or) \(\frac{1}{z}\) ⇒ Z^-1 = \(\frac{1}{1-i}\) Multiplying and dividing with 1+i ⇒ Z^-1 = \(\frac{1}{1-i}\times \frac{1+i}{1+i}\) ⇒ Z^-1 = \(\frac{1+i}{1^2-(i)^2}\) We know that i²=-1 ⇒ Z^-1 = \(\frac{1+i}{1-(-1)}\) ⇒ Z^-1 = \(\frac{1+i}{2}\) ∴ The Multiplicative inverse of 1-i is \(\frac{1+i}{2}\)

Find the multiplicative inverse of the following complex numbers : 1 – i

Answer»

Given complex number is Z=1-i

We know that the multiplicative inverse of a complex number Z is Z^-1 (or) \(\frac{1}{z}\)

⇒ Z^-1 = \(\frac{1}{1-i}\)

Multiplying and dividing with 1+i

⇒ Z^-1 = \(\frac{1}{1-i}\times \frac{1+i}{1+i}\)

⇒ Z^-1 = \(\frac{1+i}{1^2-(i)^2}\)

We know that i²=-1

⇒ Z^-1 = \(\frac{1+i}{1-(-1)}\)

⇒ Z^-1 = \(\frac{1+i}{2}\)

∴ The Multiplicative inverse of 1-i is \(\frac{1+i}{2}\)