Complex Numbers Flashcardizz GPS

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 i^2 = -1.

Front

What is the imaginary unit 'i'?

Back

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.

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.

Front

What is the product of two complex numbers (a + bi)(c + di)?

Back

The product is given by (a + bi)(c + di) = ac + adi + bci + bdi^2 = (ac - bd) + (ad + bc)i.

Front

What is the conjugate of a complex number?

Back

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

Front

How do you multiply a complex number by its conjugate?

Back

Multiplying a complex number by its conjugate results in a real number: (a + bi)(a - bi) = a^2 + b^2.

Front

What is the simplified form of (8 - 3i)^2?

Back

The simplified form is 55 - 48i.

Front

Simplify: (7 + 2i)(9 - 6i)

Back

The simplified form is 75 - 24i.

Front

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

Back

The result is 5 + 14i.