Find the multiplicative inverse of the following complex numbers :

(1 + i √3)2

Given complex number is Z=(1+i)2


⇒ Z=12+(i)2+2(1)(i)


⇒ Z=1+3i2+2i


We know that i2=-1


⇒ Z=1+3(-1)+2i


⇒ Z=-2+2i


We know that the multiplicative inverse of a complex number Z is .


⇒


Multiplying and dividing with -2-2i


⇒


⇒


⇒


⇒


⇒


∴ The Multiplicative inverse of (1+i)2 is .


4