Introduction to 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 and b are real numbers, and i is the imaginary unit, defined as the square root of -1.

Front

What is the imaginary unit 'i'?

Back

Front

How do you add two complex numbers?

Back

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

Front

Calculate: (4 - 7i) - (-3 + 6i)

Back

7 - 13i

Front

Simplify the expression: (8 + 9i) + (4 - 6i)

Back

12 + 3i

Front

What is the result of subtracting 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

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

Back

2 - 2i

Front

What is the square root of a negative number?

Back

Front

Back

Front

What is the conjugate of a complex number?

Back

The conjugate of a complex number a + bi is a - bi. It is used in division and simplifying expressions.