Advertisement Remove all ads

Write the Least Positive Integral Value of N for Which ( 1 + I 1 − I ) N is Real. - Mathematics

Write the least positive integral value of n for which  \[\left( \frac{1 + i}{1 - i} \right)^n\] is real.

Advertisement Remove all ads

Solution

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

\[ = \left( \frac{1 + i}{1 - i} \times \frac{1 + i}{1 + i} \right)^n \]

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

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

\[ \Rightarrow \left( \frac{2i}{2} \right)^n \]

\[ = i^n \]

\[\text { For } i^n \text { to be real, the smallest positive value of n will be 2 } . \]

\[\text { As }, i^2 = - 1, \text{ which is real} .\]

  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
Q 10 | Page 62
Advertisement Remove all ads

Video TutorialsVIEW ALL [1]

Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×