Complex Numbers?

Front

Define 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 i² = -1.

Front

What is the imaginary unit?

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?

Back

To multiply complex numbers, use the distributive property (FOIL). For example, (a + bi)(c + di) = ac + adi + bci + bdi² = (ac - bd) + (ad + bc)i.

Front

Back

Front

Find the sum: (5-2i) + (-7+8i)

Back

The sum is -2 + 6i.

Front

Multiply: (4 – 3i)(7 + 2i)

Back

The product is 34 - 13i.

Front

Simplify: (-10 + 4i) - (15 - 14i)

Back

The result is -25 + 18i.

Front

Solve the equation: 4x² - 25 = 0

Back

The solutions are x = 5/2 and x = -5/2.