Advertisement Remove all ads

Express the Following Complex Number in the Standard Form A + I B:\[\Frac{(1 - I )^3}{1 - I^3}\] - Mathematics

Express the following complex number in the standard form a + i b:

\[\frac{(1 - i )^3}{1 - i^3}\]

Advertisement Remove all ads

Solution

\[ \frac{\left( 1 - i \right)^3}{1 - i^3}\]

\[\frac{\left( 1 + i^2 - 2i \right)\left( 1 - i \right)}{1 - i^3} \left( \because i^2 = - 1 \right)\]

\[\frac{- 2i\left( 1 - i \right)}{1 - i^3}$\times$\frac{1 + i^3}{1 + i^3}\]

\[\frac{- 2i\left( 1 + i^3 - i - i^4 \right)}{1 - i^6}\]

\[\frac{- 2i\left( 1 - i - i - 1 \right)}{1 - i^2}\]

\[\frac{- 2i\left( - 2i \right)}{2}\]

\[ = - 2 + 0i\]

  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 1.08 | Page 31
Advertisement Remove all ads

Video TutorialsVIEW ALL [1]

Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×