HW: Flashcardizz: Complex numbers

Front

What is a complex number?

Back

A complex number is a number that has a real part and an imaginary part, usually written in the form a + bi, where a is the real part and b is the imaginary part.

Front

What does 'i' represent in complex numbers?

Back

The letter 'i' represents the imaginary unit, which is defined as the square root of -1.

Front

What is the value of i^2?

Back

The value of i^2 is -1.

Front

How do you simplify the square root of a negative number?

Back

Front

What is the product of two imaginary numbers, like (3i)(2i)?

Back

The product of two imaginary numbers is a real number. For example, (3i)(2i) = 6i^2 = 6(-1) = -6.

Front

What is the simplified form of (-6i)(3i)?

Back

The simplified form is 18.

Front

What is the result of multiplying a complex number by a real number?

Back

The result is another complex number. For example, (2 + 3i)(4) = 8 + 12i.

Front

How do you add two complex numbers?

Back

To add two complex numbers, you add their real parts and their imaginary parts separately. For example, (2 + 3i) + (4 + 5i) = (2 + 4) + (3 + 5)i = 6 + 8i.

Front

What is the conjugate of a complex number?

Back

The conjugate of a complex number a + bi is a - bi. It changes the sign of the imaginary part.

Front

What happens when you multiply a complex number by its conjugate?

Back

When you multiply a complex number by its conjugate, the result is a real number. For example, (a + bi)(a - bi) = a^2 + b^2.