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).

Tags

CCSS.HSN.CN.A.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.

Tags

CCSS.HSN.CN.A.1

Front

Simplify: 2i - 7i + 10

Back

-5i + 10

Tags

CCSS.HSN.CN.A.2

Front

Multiply: (2i)(3i)

Back

-6

Tags

CCSS.HSN.CN.A.2

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.

Tags

CCSS.HSN.CN.A.3

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.

Tags

CCSS.HSN.CN.A.2