Warm-up 3.6-1

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 the square root of -1.

Front

What is 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 include complex numbers.

Front

What is the complex conjugate of a complex number?

Back

The complex conjugate of a complex number a + bi is a - bi, where a and b are real numbers.

Front

How do you multiply complex conjugates?

Back

To multiply complex conjugates (a + bi)(a - bi), use the formula: a^2 + b^2.

Front

What is the result of multiplying (3 - 2i)(3 + 2i)?

Back

The result is 13.

Front

What is the conjugate of the complex number 2 + i√3?

Back

The conjugate is 2 - i√3.

Front

How do you multiply square roots of negative numbers?

Back

To multiply square roots of negative numbers, express them in terms of 'i'. For example, √(-8) = 2i√2.

Front

What is the result of multiplying 2√(-8) and 3√(-2)?

Back

The result is 24i.

Front

What is the Complex Conjugate Root Theorem?

Back

The Complex Conjugate Root Theorem states that if a polynomial has real coefficients and a complex root a + bi, then its complex conjugate a - bi is also a root.

Front

If 3 + 5i is a root of a polynomial, what is another root?

Back

Another root is 3 - 5i.