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 represent the square root of negative numbers.

Front

What is the sum of (5 - 2i) + (-7 + 8i)?

Back

-2 + 6i

Front

What is the sum of (1 - 2i) + (-4 + 2i)?

Back

-3

Front

What is the result of simplifying 2i - 7i + 10?

Back

10 - 5i

Front

What is the product of (1 - 2i)(6 + 5i)?

Back

16 - 7i

Front

How do you add two complex numbers?

Back

To add two complex numbers, combine their real parts and their imaginary parts separately.

Front

How do you subtract two complex numbers?

Back

To subtract two complex numbers, subtract their real parts and their imaginary parts separately.

Front

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

Back

The conjugate of a complex number a + bi is a - bi.

Front

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

Back

The modulus of a complex number a + bi is given by √(a² + b²).