Complex Number Operations 23-24 R

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 i^2 = -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, which means i^2 = -1.

Tags

CCSS.HSN.CN.A.1

Front

How do you add two complex numbers?

Back

To add two 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

Front

How do you subtract two complex numbers?

Back

To subtract two complex numbers, subtract 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

Front

What is the product of two complex numbers (a + bi)(c + di)?

Back

The product is given by (a + bi)(c + di) = ac + adi + bci + bdi^2 = (ac - bd) + (ad + bc)i.

Tags

CCSS.HSN.CN.A.2

Front

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

Back

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

Tags

CCSS.HSN.CN.A.3

Front

How do you multiply a complex number by its conjugate?

Back

Multiplying a complex number by its conjugate results in a real number: (a + bi)(a - bi) = a^2 + b^2.

Tags

CCSS.HSN.CN.A.2

Front

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

Back

The modulus (or absolute value) of a complex number a + bi is given by |a + bi| = √(a^2 + b^2).

Front

Simplify: (-2 + i)^2

Back

3 - 4i.

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CCSS.HSN.CN.C.8

Front

Calculate: 4i(-2 - 8i)

Back

32 - 8i.

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CCSS.HSN.CN.A.2