Complex Conjugates

Front

What are complex conjugates?

Back

Complex conjugates are pairs of complex numbers of the form a + bi and a - bi, where a and b are real numbers.

Tags

CCSS.HSN.CN.A.3

Front

How do you simplify a complex number?

Back

To simplify a complex number, combine like terms and express it in the form a + bi.

Tags

CCSS.HSN.CN.A.1

Front

What is the result of multiplying a complex number by its conjugate?

Back

The result is a real number: (a + bi)(a - bi) = a^2 + b^2.

Tags

CCSS.HSN.CN.C.8

Front

What is the significance of complex conjugates in division?

Back

Complex conjugates are used to eliminate the imaginary part in the denominator when dividing complex numbers.

Tags

CCSS.HSN.CN.A.3

Front

Simplify: (4 + 3i) + (2 - 5i)

Back

6 - 2i.

Tags

CCSS.HSN.CN.A.2

Front

Simplify: (3 + 4i) - (1 + 2i)

Back

2 + 2i.

Tags

CCSS.HSN.CN.A.2

Front

What is the formula for the modulus of a complex number?

Back

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

Front

How do you express a complex number in polar form?

Back

A complex number can be expressed in polar form as r(cos θ + i sin θ), where r is the modulus and θ is the argument.

Tags

CCSS.HSN.CN.B.4

Front

What is the argument of a complex number?

Back

The argument of a complex number a + bi is the angle θ formed with the positive x-axis, calculated as θ = arctan(b/a).

Front

Simplify: (2 + 3i)(2 - 3i)

Back

The result is 13.

Tags

CCSS.HSN.CN.C.8