Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • Multiplicative inverse of complex number    is<div class='qn

Multiplicative inverse of complex number  z=\frac{5+i\sqrt2}{1-i\sqrt2}  is

Option: 1

\\\frac{1-8i\sqrt2}{9}


Option: 2

\\\frac{1-2i\sqrt2}{9}


Option: 3

\\\frac{1-2i\sqrt2}{3}


Option: 4

\\\frac{1+2i\sqrt2}{9}


Answers (1)

best_answer

As we have learnt, 

The multiplicative inverse of z is 1/z

Now,

\\z=\frac{5+i\sqrt2}{1-i\sqrt2} \\So \,\,\,\frac{1}{z}= \frac{1-i\sqrt2}{5+i\sqrt2}\\\\ =\frac{1-i\sqrt2}{5+i\sqrt2}. \frac{5-i\sqrt2}{5-i\sqrt2}\\\\ =\frac{5-i\sqrt2-i5\sqrt2-2}{25 + 2}\\\\ =\frac{3-6\sqrt2i}{27} \\\\ =\frac{3(1-2\sqrt2i)}{27}\\\\ =\frac{(1-2\sqrt2i)}{9}

So the multiplication inverse is \\\frac{1-2i\sqrt2}{9}.

option (b) is correct

Posted by

vinayak

View full answer

Similar Questions