Operations of 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

What is the product of two complex conjugates (a + bi)(a - bi)?

Back

The product of two complex conjugates is a² + b².

Front

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

Back

To add two complex numbers, combine the real parts and the imaginary parts: (a + c) + (b + d)i.

Front

How do you subtract two complex numbers (a + bi) - (c + di)?

Back

To subtract two complex numbers, subtract the real parts and the imaginary parts: (a - c) + (b - d)i.

Front

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

Back

The result is -12 - 6i.

Front

What is the sum of the complex numbers (2 + 5i) and (2 - 5i)?

Back

The sum is 4.

Front

What does i² equal?

Back

i² equals -1.

Front

What is the result of simplifying (12 - 4i) + (-2 + 8i)?

Back

The result is 10 + 4i.

Front

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

Back

The modulus is √(a² + b²).