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 fraction?

Back

To simplify a complex fraction, multiply the numerator and the denominator by the conjugate of the denominator.

Front

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

Back

The result is a real number, specifically the sum of the squares of the real and imaginary parts.

Front

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

Back

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

Front

How do you express a complex number in standard form?

Back

A complex number is in standard form when it is expressed as a + bi, where a is the real part and b is the imaginary part.

Tags

CCSS.HSN.CN.A.1

Front

What is the significance of the imaginary unit 'i'?

Back

The imaginary unit 'i' is defined as the square root of -1, and it is used to extend the real number system to complex numbers.

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.

Tags

CCSS.7.NS.A.1C

Front

How do you subtract two complex numbers?

Back

To subtract two complex numbers, subtract their real parts and their imaginary parts separately.

Tags

CCSS.HSN.CN.A.2

Front

What is the process for multiplying two complex numbers?

Back

To multiply two complex numbers, use the distributive property (FOIL) and combine like terms.

Front

What is the division of complex numbers?

Back

To divide complex numbers, multiply the numerator and denominator by the conjugate of the denominator and simplify.

Tags

CCSS.HSN.CN.A.3