Step by step video & image solution for If alpha_1, alpha_2, alpha_3, alpha_4 are the roots of the equation x^4+ (2-sqrt3)x^2+2+sqrt3=0 then find the value of (1-alpha_1) (1-alpha_2) (1 …

Suppose α1, α2, α3, α4 α 1, α 2, α 3, α 4 are the roots of the equation x4 + x2 + 1 = 0. x 4 + x 2 + 1 = 0. Then, find the sum of each roots raised to the 4th power.

Definition 2 A complex number 3 is a number of the form a + bi where a and b are real numbers. If. z = a + bi then a is known as the real part of z and b as the imaginary part. We write a = Re …

Outcomes Understand De Moivre’s theorem and be able to use it to find the roots of a complex number.

Since rules of algebra hold for complex numbers as well as for real numbers, the quadratic formula correctly gives the roots of a quadratic equation x2 + bx + c = 0 even when the …

If α1< α2< α3< α4< α5< α6, then the equation (x-α1) (x-α3) (x-α5)+3 (x-α2) (x-α4) (x-α6)=0 has - (A) three real roots (B) no real root in (-∞

COMPLEX NUMBERS 5.1 Constructing the complex numbers One way of introducing the field C of complex numbers is via the arithmetic of 2 × 2 matrices. DEFINITION 5.1.1 A complex …

If α1,α2,α3,α4 are the roots of the equation x4+(2− 3)x2+2+ 3=0, then the value of (1−α1)(1− α2)(1−α3)(1−α4) is. State true or false for the following. (i) The order relation is defined on the …

Two complex numbers are equal if and only if their real parts are equal and their imaginary parts are equal. We represent complex numbers graphically by associating z = a + bi z = a + b i with …

To solve the problem, we need to evaluate the expression: ω−α1 ω2−α1 ⋅ ω−α2 ω2−α2 ⋅ ω−α3 ω2−α3 ⋅ ω−α4 ω2−α4. where ω is the imaginary cube root of unity, and α1,α2,α3,α4 are the …