Front

Define complex numbers.

Back

Complex numbers are numbers that have a real part and an imaginary part, expressed in the form a + bi, where a is the real part, b is the imaginary part, 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 express complex numbers.

Tags

CCSS.HSN.CN.A.1

Front

How do you add complex numbers?

Back

To add complex numbers, combine 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 complex numbers?

Back

To subtract 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

Simplify the expression: (5 + 4i) - (-1 - 2i)

Back

6 + 6i.

Tags

CCSS.HSN.CN.A.2

Front

Calculate: (4 - 7i) - (-3 + 6i)

Back

7 - 13i.

Tags

CCSS.HSN.CN.A.2

Front

Calculate: i + 6i

Back

7i.

Tags

CCSS.HSN.CN.A.2

Front

Simplify the expression: (1 + 5i) + (1 - 5i)

Back

2.

Tags

CCSS.HSN.CN.A.2

Front

Simplify the expression: (8 + 9i) + (4 - 6i)

Back

12 + 3i.

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