Home
Class 12
MATHS
If i z^4+1=0, then prove that z can take...

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

A

`(1+i)/(sqrt(2))`

B

`cos""((pi)/(8))+isin""((pi)/(8))`

C

`(1)/(4i)`

D

`i`

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    ARIHANT MATHS|Exercise Exercise For Session 4|14 Videos

  • COMPLEX NUMBERS

    ARIHANT MATHS|Exercise Exercise (Single Option Correct Type Questions)|30 Videos

  • COMPLEX NUMBERS

    ARIHANT MATHS|Exercise Exercise For Session 2|14 Videos

  • CIRCLE

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|16 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|20 Videos

Similar Questions

Explore conceptually related problems

If iz^3+z^2-z+i = 0 , then show that |z|=1.

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

1. If |z-2+i| ≤ 2 then find the greatest and least value of | z|

If |z-4/z|=2 then the greatest value of |z| is:

If z^3+(3+2i)z+(-1+i a)=0 has one real roots, then the value of a lies in the interval (a in R)

If tan^-1 x + tan^-1y - tan^-1z = 0 , then prove that x + y + xyz = z.

If z^2+z+1=0 where z is a complex number, then the value of (z+1/z)^2+(z^2+1/z^2)^2+....+(z^6+1/z^6)^2 is

Let z be a complex number such that the imaginary part of z is nonzero and a = z^(2) + z+z+1 is real. Then a cannot take the value.

If z = 2-3i , show that z^2- 4z+13= 0 and hence find the value of 4z^3 - 3z^2 + 169 .

If z_(1),z_(2),z_(3) andz_(4) are the roots of the equation z^(4)=1, the value of sum_(i=1)^(4)z_i^(3) is