Operations with Complex Numbers

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 i = √-1. It is used to represent the square root of negative numbers.

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

What is the result of (3 + 2i) + (4 - 5i)?

Back

The result is 7 - 3i.

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 product of two complex numbers?

Back

To multiply two complex numbers, use the distributive property (FOIL method). For example, (a + bi)(c + di) = ac + adi + bci + bdi², and since i² = -1, combine like terms.

Front

What is the result of (3 + 8i)(-2 - i)?

Back

The result is 2 - 19i.

Front

What is the modulus of a complex number?

Back

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

Front

What is the conjugate of a complex number?

Back

The conjugate of a complex number a + bi is a - bi. It is used in division and to find the modulus.

Front

What is the result of (-5 + 10i)(-5 - 10i)?

Back

The result is 125.