Quiz 1 (Complex Numbers)

Recognise that , therefore   (shown)

The value of k is 71 because the question states that the roots of the quadratic equation are where k is a positive integer. Therefore, since k is a positive integer and the only option given is 71, the value of k must be 71.

not-available-via-ai

not-available-via-ai

Note that the property is used here:

(2+i)(2-i)(3+i)(3-i) = [(2+i)(2-i)] [(3+i)(3-i)] = (5)(10)=50 (shown)

The statement is false because a quadratic equation can have either two distinct real roots or two complex conjugate roots. It cannot have three pairs of complex conjugate roots as that would imply a total of six roots, which is not possible for a quadratic equation.

The given equation represents the perpendicular bisector of a line segment in the Argand space. The perpendicular bisector is a line that intersects the line segment at a right angle and divides it into two equal parts. Since the equation does not represent a circle, the concept of radius does not apply. Therefore, the correct answer is "It is not a circle but a perpendicular bisector."