Complex Numbers and Their Properties

The video tutorial explores complex graphs, starting with simple examples and their properties, such as circles with a given radius and center. It then delves into inequalities in complex numbers, focusing on algebraic solutions. The tutorial progresses to vectors, explaining position vectors and their geometric implications. It further discusses calculating distances between complex numbers and concludes with finding the locus of points equidistant from two points, emphasizing the concept of perpendicular bisectors.

What is the shape of the graph described by the equation |z| = 2 in the complex plane?

• A hyperbola

• A circle

• A parabola

• A line

Where is the center of the circle described by the equation |z| = 2?

• At the origin

• At (2, 0)

• At (0, 2)

• At (1, 1)

When tackling inequalities in the complex plane, what happens to the imaginary components?

• They double

• They cancel out

• They become zero

• They remain unchanged

In the context of vectors, what does the position vector represent?

• The sum of two vectors

• The direction of a vector

• The distance from the origin

• The difference between two points

What is the result of subtracting one complex number from another in terms of vectors?

• A scalar value

• A zero vector

• A position vector

• A new complex number

How is the distance between a complex number and the origin represented?

• As the real part of the complex number

• As the imaginary part of the complex number

• As the modulus of the complex number

• As the sum of the real and imaginary parts

What does changing the point of reference in the complex plane involve?

• Changing the modulus

• Changing the origin

• Changing the imaginary unit

• Changing the real axis

What is the locus of points equidistant from two complex numbers?

• A perpendicular bisector

• A circle

• A line

• A parabola

What is the gradient of the line that is the perpendicular bisector of two points in the complex plane?

• 1

• 2

• -1

• 0

What is the equation of the line that is the perpendicular bisector of the points 2i and -1 + i?

• y = x - 1

• y = -x - 1

• y = -x + 1

• y = x + 1