Front

What is 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 the square root of -1.

Front

What is the imaginary unit 'i'?

Back

The imaginary unit 'i' is defined as the square root of -1. It is used to extend the real number system to include solutions to equations that do not have real solutions.

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.

Front

How do you subtract two complex numbers?

Back

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

Front

What is the conjugate of a complex number?

Back

The conjugate of a complex number a + bi is a - bi. It is obtained by changing the sign of the imaginary part.

Front

What is the modulus of a complex number?

Back

The modulus of a complex number a + bi is given by the formula |a + bi| = √(a² + b²). It represents the distance of the complex number from the origin in the complex plane.

Front

How do you find the modulus of the complex number 3 + 4i?

Back

The modulus is |3 + 4i| = √(3² + 4²) = √(9 + 16) = √25 = 5.

Front

What is the real part of a complex number?

Back

The real part of a complex number a + bi is the value 'a'. It represents the horizontal component in the complex plane.

Front

What is the imaginary part of a complex number?

Back

The imaginary part of a complex number a + bi is the value 'b'. It represents the vertical component in the complex plane.

Front

How do you express a complex number in polar form?

Back

A complex number can be expressed in polar form as r(cos θ + i sin θ), where r is the modulus and θ is the argument (angle) of the complex number.