LIVE Course for free

Rated by 1 million+ students
Get app now
0 votes
195 views
in Complex Numbers by (30.0k points)
closed by
What is the modulus of the complex number i2n + 1(-i)2n - 1, where n ∈ N and i = √-1?
1. 1
2. - 1
3. √2
4. 2

1 Answer

0 votes
by (54.3k points)
selected by
 
Best answer
Correct Answer - Option 1 : 1

Concept:

Iota power:

  • i2 = -1, i3 = -i, i4 = 1
  • Number of the form 2n is always even, n ∈ N
  • Numebr of the form 2n +1 or 2n - 1 is always odd, n ∈ N
  • (-a)2n -1 = -(a)2n -1

Calculation:

Given:

i2n + 1(-i)2n - 1

From the concept used we know that 2n - 1 is odd

⇒ i2n + 1(-i)2n - 1

 - (i)2n + 1(i)2n - 1

 - (i)2n + 1 + 2n - 1

⇒ - (i)4

- (i4)n

 - (1) = -1

Hence, the modulus of the complex number i2n + 1(-i)2n - 1 is  1.

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

...