Home
Class 12
MATHS
Simplifiy i^(2)+i^(4)+i^(6)+.....+(2n...

Simplifiy
`i^(2)+i^(4)+i^(6)+.....+(2n+1)` terms

Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    VIKRAM PUBLICATION ( ANDHRA PUBLICATION)|Exercise EXERCISE -1 (C)|29 Videos

  • COMPLEX NUMBERS

    VIKRAM PUBLICATION ( ANDHRA PUBLICATION)|Exercise EXERCISE -1 (D)|13 Videos

  • COMPLEX NUMBERS

    VIKRAM PUBLICATION ( ANDHRA PUBLICATION)|Exercise EXERCISE -1 (A)|11 Videos

  • CIRCLE

    VIKRAM PUBLICATION ( ANDHRA PUBLICATION)|Exercise EXERCISE - 1(e)|25 Videos

  • DE MOIVRE'S THEOREM

    VIKRAM PUBLICATION ( ANDHRA PUBLICATION)|Exercise Long Answer Questions|6 Videos

Similar Questions

Explore conceptually related problems

i+ i^(2) + i^(3) + i^(4) + …. + i^(100)

1+i^2+i^4+i^6+.........+i^(2n)=

Simplifiy i^(18)-3.i+i^(2)(1+i^(4))(-i)^(26)

Simplify i^18-3i^7 +i^2 (1 +i^4) (-i)^26 .

I : i^2+i^4+i^6+......(2n+1) terms = - 1 II : 1+i^2+i^4+i^6+......i^(2n)=0

i+ 2i^(2) + 3i^(3) + 4i^(4) + …. + 100i^(100) =

Simplify -2i(3+i)(2+4i)(1+i) and obtain the modulus of that complex number.

If i= sqrt-1 and n is a positive integer , then i^(n) + i^(n + 1) + i^(n + 2) + i^(n + 3) is equal to

If n is integer then show that (1 + i)^(2n) + (1 - i)^(2n) = 2 ^(n+1) cos . (npi)/2 .

VIKRAM PUBLICATION ( ANDHRA PUBLICATION)-COMPLEX NUMBERS-EXERCISE -1 (B)
  1. Write the conjugate of the complex numbers (2+5i)(-4+6i)

    Text Solution

    |

  2. Write the conjugate of the complex numbers (5i)/(7+i)

    Text Solution

    |

  3. Simplifiy i^(2)+i^(4)+i^(6)+.....+(2n+1) terms

    Text Solution

    |

  4. Simplifiy i^(18)-3.i+i^(2)(1+i^(4))(-i)^(26)

    Text Solution

    |

  5. Find the square root of the following complex number: -8-6i

    Text Solution

    |

  6. Find a square root for the complex numbers. (3+4i)

    Text Solution

    |

  7. Find a square root for the complex numbers. (-47+i8 sqrt(3))

    Text Solution

    |

  8. Find the multiplicative inverse of the complex numbers. sqrt(5)+3i

    Text Solution

    |

  9. Find the multiplicative inverse of the complex numbers. -i

    Text Solution

    |

  10. Find the multiplicative inverse of the complex numbers. i^(-35)

    Text Solution

    |

  11. If (a+ib)^(2)=x+iy, find x^(2)+y^(2)

    Text Solution

    |

  12. If x+iy=3/(2+costheta +i sin theta), then show that x^2+y^2=4x-3

    Text Solution

    |

  13. If x+iy=(1)/(1+ cos theta+ isin theta), show that 4x^(2)-1=0

    Text Solution

    |

  14. If u+iv=(2+i)/(z+3) and z=x+iy find u, v

    Text Solution

    |

  15. If z=3-5i Show that z^(3)-10z^(2)+58z-136=0

    Text Solution

    |

  16. If z=2-isqrt(7), then show that 3z^(3)-4z^(2)+z+88=0

    Text Solution

    |

  17. Show that (2-i)/((1-2i)^(2)) and ((-2-11 i)/(25)) are conjugate to eac...

    Text Solution

    |

  18. (x+iy)^(1/3) =(a+ib) then prove that (x/a+y/b)=4(a^2-b^2)

    Text Solution

    |

  19. Write ((a+ib)/(a-ib))^(2)-((a-ib)/(a+ib))^(2) in the fom of x+iy

    Text Solution

    |

  20. If x and y are real numbers of such that ((1+i)x-2i)/(3+i)+((2-3i)y+i...

    Text Solution

    |