Imaginary Numbers

Front

What is an imaginary number?

Back

An imaginary number is a number that can be written as a real number multiplied by the imaginary unit 'i', where i is 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 extend the real number system to include solutions to equations that do not have real solutions.

Front

What is the sum of (4 + 7i) and (3 + 2i)?

Back

The sum is 7 + 9i.

Front

What is the difference of (4 + 7i) and (3 + 2i)?

Back

The difference is 1 + 5i.

Front

What is the result of (2 - 4i) + (5 + 6i)?

Back

The result is 7 + 2i.

Front

What is the result of (2 - 4i) - (5 + 6i)?

Back

The result is -3 - 10i.

Front

What is the product of (2 + 3i) and (1 - 2i)?

Back

The product is 8 - i.

Front

What is the conjugate of the complex number 3 + 4i?

Back

The conjugate is 3 - 4i.

Front

What is the modulus of the complex number 3 + 4i?

Back

The modulus is √(3² + 4²) = 5.

Front

What is the simplified form of √(-10)?

Back

The simplified form is ±√10i.