The imaginary unit i is defined as i² = ___?

-1

True or False: The sum of the roots of the quadratic equation ax² + bx + c = 0 is given by -c/a.

False. The sum of the roots is given by -b/a.

If z₁ and z₂ are two complex numbers, their modulus satisfies the property |z₁z₂| = ___?

|z₁| × |z₂|

The quadratic equation ax² + bx + c = 0 has roots given by the formula x = ___, where D = b² - 4ac.

(-b ± √D) / (2a)

True or False: If the discriminant D of a quadratic equation is less than zero, then the roots are real and unequal.

False. If D < 0,="" the="" roots="" are="" />

The modulus of a complex number z = x + iy is given by |z| = ___?

√(x² + y²)

If a and b are the roots of the quadratic equation ax² + bx + c = 0, then the product of the roots can be expressed as ___?

C/a

For a complex number z = a + ib, the real part is denoted as ___?

Re(z) = a

True or False: The argument of a complex number z = x + iy is always a unique value.

False. The argument is not unique; it can differ by multiples of 2π.

The polar form of a complex number z = x + iy can be expressed as z = ___?

R(cos(θ) + isin(θ)) where r = |z| and θ = arg(z)

The distance between two complex numbers z₁ and z₂ represented by points P and Q in the Argand plane is given by |z₁ - z₂| = ___?

√((x₂ - x₁)² + (y₂ - y₁)²)

If the quadratic equation ax² + bx + c = 0 has roots α and β, then the relation between roots and coefficients gives us α + β = ___?

-b/a

True or False: The cube roots of unity are 1, ω, ω², where ω = e^(2πi/3).

True.

The condition for a quadratic equation to have equal roots is ___?

D = 0, where D = b² - 4ac.

Fill in the blank: The argument of a complex number z = x + iy is given by ___, where x and y are the real and imaginary components of z, respectively.

Arg(z) = tan⁻¹(y/x)