Powers of i and Complex Numbers

Front

What is the definition of a complex number?

Back

A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers, and i is the imaginary unit, defined as i = √(-1).

Front

What is the imaginary unit 'i'?

Back

The imaginary unit 'i' is defined as the square root of -1, i.e., i = √(-1). It is used to extend the real number system to complex numbers.

Front

In which quadrant is the complex number -2 + 5i located?

Back

The complex number -2 + 5i is located in Quadrant II.

Front

How do you represent the complex number 3 - 4i in coordinate form?

Back

The complex number 3 - 4i can be represented as the point (3, -4) in the complex plane.

Front

Where is the complex number 4i located on the complex plane?

Back

The complex number 4i is located on the Y-Axis.

Front

What is the distance from the origin to the point B (5, 0) in the complex plane?

Back

The distance from the origin to point B (5, 0) is 5.

Front

What is the distance from the origin to the point A (3, 4) in the complex plane?

Back

Front

What is the modulus of a complex number z = a + bi?

Back

Front

What is the conjugate of a complex number z = a + bi?

Back

The conjugate of a complex number z = a + bi is given by z* = a - bi.

Front

How do you add two complex numbers?

Back

To add two complex numbers, add their real parts and their imaginary parts separately. For example, (a + bi) + (c + di) = (a + c) + (b + d)i.