Home
Class 12
MATHS
The least positive integer 'n' for which...

The least positive integer 'n' for which `(1+i)^n = (1 - i)^n` holds is

A

8

B

16

C

12

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
Since `((1+i)/(1-i))^n=1 rArr ((1+i)/(1-i)xx(1+i)/(1+i))^n = 1`
`rArr ((2i)/2)^n=1`
`rArr " " i^n=1`
The smallest positive interger n for which `i^n=1 ` is 4.
`therefore " "n=4`
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    IIT JEE PREVIOUS YEAR|Exercise TOPIC 2 CONJUGATE AND MODULUS OF A COMPLEX NUMBER (OBJECTIVE QUESTION I)(Only one correct option )|25 Videos

  • COMPLEX NUMBERS

    IIT JEE PREVIOUS YEAR|Exercise TOPIC 2 CONJUGATE AND MODULUS OF A COMPLEX NUMBER (PASSAGE BASED PROBLEMS )(PASSAGE I)|3 Videos

  • CIRCLE

    IIT JEE PREVIOUS YEAR|Exercise Topic 5 Integer Answer type Question|1 Videos

  • DEFINITE INTEGRATION

    IIT JEE PREVIOUS YEAR|Exercise LIMITS AS THE SUM|6 Videos

Similar Questions

Explore conceptually related problems

The smallest positive integer n forwhich ((1 + i)/(1 - i))^(n) = 1 is:

What is the smallest positive integer n for which (1+i)^(2n)=(1-i)^(2n)?

The smallest positive integer n for which ((1 + i)/(1-i))^(n) = -1 is :

IIT JEE PREVIOUS YEAR-COMPLEX NUMBERS-TOPIC 5 DE-MOIVRES THEOREM,CUBE ROOTS AND nth ROOTS OF UNITY (INTEGER ANSWER TYPE QUESTION)
  1. The least positive integer 'n' for which (1+i)^n = (1 - i)^n holds is

    Text Solution

    |

  2. Let omega= e^((ipi)/3) and a, b, c, x, y, z be non-zero complex numb...

    Text Solution

    |