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 'i'?

Back

The imaginary unit 'i' is defined as the square root of -1, which means i² = -1.

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 imaginary units?

Back

The product of two imaginary units is i * i = i² = -1.

Front

Simplify: (4 + 7i) - (3 + 2i)

Back

1 + 5i.

Front

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

Back

-2 + 6i.

Front

Simplify: √-108

Back

6i√3.

Front

Simplify: -3i(4 + 2i)

Back

6 - 12i.

Front

Multiply: (2i)(3i)

Back

-6.