Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
BITSAT 2023Paper 1
Exam
BITSAT
Year
2023
Paper
Paper 1
Subject
Mathematics
Chapter
Complex Number

BITSAT 2023 · Paper 1 · Mathematics · Complex Number

i^ 57 + 1 i^ 25 , when simplified has the value

i57+1i25i^{57}+\frac{1}{i^{25}}, when simplified has the value

Options

  1. A0
  2. B2i2 i
  3. C−2i-2 i
  4. D2

Correct answer

A. 0

Step-by-step solution

i57+1i25=(i4)14.i+1(i4)6.i=i+1i=i−i=0i^{57}+\frac{1}{i^{25}}=\left(i^4\right)^{14}. i+\frac{1}{\left(i^4\right)^6.i}=i+\frac{1}{i}=i-i=0
Practice Complex Number on Quantrex Academy →

More from Complex Number

The points represented by the complex number 1+i,-2+3 i, (5)/(3) i on the argand plane are BITSAT 2024The modulus of the complex number z such that |z+3-i|=1 and (z)=π is equal to BITSAT 2024If z, z ,-z,- z forms a rectangle of area 2 3 square units, then one such z is BITSAT 2024If z_1, z_2, … . . z_n are complex numbers such that |z_1|=|z_2|=… . .=|z_n|=1 , then… BITSAT 2024If |z_1|=2,|z_2|=3,|z_3|=4 and |2 z_1+3 z_2+4 z_3|= 4 , then absolute value of 8 z_2… BITSAT 2024The modulus of (1+i 3 )(2+2 i) ( 3 -i) is BITSAT 2023If |w|=2 , then the set of points z=w-(1)/(w) is contained in or equal to the set of… BITSAT 2022The smallest positive integral value of n such that [(1+ (π)/(8)+i (π)/(8))/(1+ (π)/(8)-i… BITSAT 2022If z is a complex number such that z^ 2 =( z )^ 2 , then BITSAT 2021If z_ 1 = 2 [ (π)/(4)+i (π)/(4)] and z_ 2 = 3 [ (π)/(3)+ i (π)/(3)] then | z_ 1 z_ 2 |is… BITSAT 2021If |z_ 1 |=|z_ 2 |=… … … . .|z_ n |=1, then the value of |z_ 1 +z_ 2 +… … . z_ n |-| 1 z_… BITSAT 2020The value of λ for which the loci argz = (π)/(6) and | z - 2 3 i | = λ on the argand… BITSAT 2019If z _ 1 and ¯ z 1 represents adjacent vertices of a regular polygon of n sides and if… BITSAT 2019The n^ th roots of unity are in BITSAT 2018If z = a + ib satisfies arg ( z - 1 ) = arg ( z + 3i ) , then ( a - 1 ) : b = BITSAT 2017If z _ 1 , z _ 2 and z _ 3 represent the vertices of an equilateral triangle such that |… BITSAT 2017 Full Complex Number list Complex Number JEE Maths PYQsJEE Mathematics PYQs All BITSAT PYQs