It is given that the roots of the equation x2 - 4x - log3(P) = 0 are real. For this, the minimum value of P is
1
If are the roots of the equation 3x2 + 2x + 1 = 0, then the equation whose roots are is :
3x2 + 8x + 16 = 0
3x2 - 8x - 16 = 0
3x2 + 8x - 16 = 0
x2 + 8x + 16 = 0
Suppose is a cube root unity with . Suppose P and Q are the points on the complex plane defined by . If O is the origin,then what is the angle between OP and OQ ?
Let z1 , z2 and z3 be non-zero complex numbers satisfying
z2 = iz, where i = .
What is z1 + z2 + z3 = ?
i
- i
0
1
C.
0
Denote conjugate of z by z*
We are given z2= i z*.
Taking modulus on both sides we see that |z2| = |z|
since z is non-zero, we have |z| = 1
i.e. zz* = 1 or z* = 1/z.
Given equation is z2= iz*
or z2 = i/z (since z* = 1/z)
or z3 - i = 0.
This is a cubic with 3 roots, and the sum of roots is 0.
i.e. z1 + z2 + z3 = 0