Advertisement Remove all ads

Find the multiplicative inverse of the following complex number: ( 1 + i √ 3 ) 2 - Mathematics

Find the multiplicative inverse of the following complex number:

\[(1 + i\sqrt{3} )^2\]

Advertisement Remove all ads

Solution

\[ z = \left( 1 + \sqrt{3}i \right)^2 \]

\[ = 1 + 3 i^2 + 2\sqrt{3}i\]

\[ = - 2 + 2\sqrt{3}i\]

\[\text { Then }, \frac{1}{z} = \frac{1}{- 2 + 2\sqrt{3}i} \times \frac{- 2 - 2\sqrt{3}i}{- 2 - 2\sqrt{3}i}\]

\[ = \frac{- 2 - 2\sqrt{3}i}{4 - 12 i^2}\]

\[ = \frac{- 2 - 2\sqrt{3}i}{16}\]

\[ = \frac{- 1}{8} - \frac{\sqrt{3}}{8}i\]

  Is there an error in this question or solution?
Advertisement Remove all ads

APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 13 Complex Numbers
Exercise 13.2 | Q 4.2 | Page 32
Advertisement Remove all ads

Video TutorialsVIEW ALL [1]

Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×