Complex Numbers

Front

Define 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

Simplify: 2i - 7i + 10

Back

-5i + 10

Front

Multiply: (2i)(3i)

Back

-6

Front

What is the square root of a negative number?

Back

Front

Back

14i

Front

Back

-6i√2

Front

What is the modulus of a complex number?

Back

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 of complex numbers.

Front

How do you add complex numbers?

Back

To add complex numbers, add their real parts and their imaginary parts separately. For example, (a + bi) + (c + di) = (a + c) + (b + d)i.