Home
Class 11
MATHS
If i z^4+1=0, then prove that z can ta...

If `i z^4+1=0,` then prove that `z` can take the value `cospi//8+isinpi//8.`

Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE ENGLISH|Exercise All Questions|365 Videos
  • CONIC SECTIONS

    CENGAGE ENGLISH|Exercise All Questions|1344 Videos

Similar Questions

Explore conceptually related problems

If i z^4+1=0, then prove that z can take the value cospi//8+is inpi//8.

If |z-1| + |z + 3| le 8 , then prove that z lies on the circle.

Prove that: 8cos^3pi/9-\ 6cospi/9=1.

Least value of |z-2|+|z-4i| is

If |z-iRe(z)|=|z-Im(z)|, then prove that z lies on the bisectors of the quadrants, " where "i=sqrt(-1).

Column I, Column II (one of the values of z ) z^4-1=0 , p. z=cospi/8+isinpi/8 z^4+1=0 , q. z=cospi/8-isinpi/8 i z^4+1=0 , r. z=cospi/4isinpi/4 i z^4-1=0 , s. z=cos0+isin0

If z_(2) be the image of a point z_(1) with respect to the line (1-i)z+(1+i)bar(z)=1 and |z_(1)|=1 , then prove that z_(2) lies on a circle. Find the equation of that circle.

If |z-1|+|z+3|<=8 , then the range of values of |z-4| is

Let complex number z satisfy |z - 2/z| =1 " then " |z| can take all values except

If z=8-2i,z^(2)=

CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. The number of complex numbers z such that |z|=1 and |z/ barz + barz/z...

    Text Solution

    |

  2. Given that x^2-3x+1=0, then the value of the expression y=x^9+x^7+x^(-...

    Text Solution

    |

  3. If i z^4+1=0, then prove that z can take the value cospi//8+isinpi//...

    Text Solution

    |

  4. Find the value of x such that ((x+alpha)^n-(x+beta)^n)/(alpha-beta)=(s...

    Text Solution

    |

  5. Suppose a ,b ,c in I such that the greatest common divisor for x^2+a ...

    Text Solution

    |

  6. Find the value of following expression: [(1-cospi/(10)+isinpi/(10))/(1...

    Text Solution

    |

  7. Dividing f(z) by z- i, we obtain the remainder i and dividing it by z...

    Text Solution

    |

  8. If the roots of the cubic equation, x^3+a x^2+b x+c=0 are three consec...

    Text Solution

    |

  9. If z1, z2 in C ,z1^2+z2^2 in R ,z1(z1^2-3z2^2)=2 and z2(3z1^2-z2^2)...

    Text Solution

    |

  10. If cosalpha+cosbeta+cosgamma=0 a n d a l so sinalpha+sinbeta+singamm...

    Text Solution

    |

  11. If x+y+z=12 andx^2+y^2+z^2=96 and 1/x+1/y+1/z=36 , then the value x^3+...

    Text Solution

    |

  12. Prove that (1+i)^n+(1-i)^n=2^((n+2)/2).cos((npi)/4), where n is a pos...

    Text Solution

    |

  13. The set {R e((2i z)/(1-z^2)): zi sacom p l e xnu m b e r ,|z|=1,z=+-1}...

    Text Solution

    |

  14. If the equation x^2+ax+bc=0" and " x^2-bx+ca=0 have a common root, the...

    Text Solution

    |

  15. If a r g["z"1("z"3-"z"2)]="a r g"["z"3("z"2-"z"1)] , then find prove t...

    Text Solution

    |

  16. If x" - "i y" "=sqrt((a-i b)/(c-i d)) prove that (x^2+y^2)^2=(a^2+b^2...

    Text Solution

    |

  17. If x^3+3x^2-9x+c is of the form (x-alpha)^2(x-beta) , then c is equ...

    Text Solution

    |

  18. If x=a+b,y=a alpha+b beta and z=abeta+ b alpha , where alpha and beta...

    Text Solution

    |

  19. If z=(a+ib)^5+(b+ia)^5 then prove that Re(z)=Im(z), where a,b in R.

    Text Solution

    |

  20. If a and b are positive numbers and eah of the equations x^2+a x+2b=0 ...

    Text Solution

    |