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 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 include solutions to equations that do not have real solutions.

Front

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

Back

The complex 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 product of a complex number and its conjugate?

Back

The product of a complex number a + bi and its conjugate a - bi is a^2 + b^2.

Front

How do you simplify the square root of a negative number, such as √-k?

Back

To simplify √-k, you can express it as i√k, where k is a positive real number.

Front

What is the simplified form of (a + bi)^2?

Back

The simplified form of (a + bi)^2 is a^2 - b^2 + 2abi.

Front

What is the sum of two complex numbers (a + bi) and (c + di)?

Back

The sum of two complex numbers (a + bi) and (c + di) is (a + c) + (b + d)i.

Front

What is the difference between two complex numbers (a + bi) and (c + di)?

Back

The difference between two complex numbers (a + bi) and (c + di) is (a - c) + (b - d)i.

Front

How do you multiply two complex numbers (a + bi) and (c + di)?

Back

To multiply two complex numbers (a + bi) and (c + di), use the distributive property: (ac - bd) + (ad + bc)i.

Front

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

Back

The modulus of a complex number a + bi is given by |a + bi| = √(a^2 + b^2).