Operations with complex numbers

Front

What is a complex number?

Back

A complex number is a number that can be expressed in the form a + bi, where a is the real part, b is the imaginary part, and i is the imaginary unit, defined as the square root of -1.

Front

How do you add complex numbers?

Back

To add complex numbers, combine the real parts and the imaginary parts separately. For example, (a + bi) + (c + di) = (a + c) + (b + d)i.

Front

What is the imaginary unit 'i'?

Back

The imaginary unit 'i' is defined as the square root of -1. It is used to express imaginary numbers.

Front

Simplify: 4i + 5i

Back

9i

Front

What is the sum of 6 + 3i and 7 + 12i?

Back

13 + 15i

Front

Find the sum of 7 + 8i and 6 - 2i.

Back

1 + 6i

Front

How do you subtract complex numbers?

Back

To subtract complex numbers, subtract the real parts and the imaginary parts separately. For example, (a + bi) - (c + di) = (a - c) + (b - d)i.

Front

Simplify: (-5 - 5i) - (-3 + 6i)

Back

-2 - 11i

Front

What is the product of two complex numbers?

Back

To multiply complex numbers, use the distributive property (FOIL method). For example, (a + bi)(c + di) = ac + adi + bci + bdi^2, and since i^2 = -1, combine like terms.

Front

Calculate: (-3 - i)(6 - i)

Back

-19 - 3i