Complex Numbers Operations

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

How do you add two complex numbers?

Back

To add two complex numbers, (a + bi) and (c + di), you add the real parts and the imaginary parts separately: (a + c) + (b + d)i.

Front

How do you subtract two complex numbers?

Back

To subtract two complex numbers, (a + bi) and (c + di), you subtract the real parts and the imaginary parts separately: (a - c) + (b - d)i.

Front

What is the result of (10 + 8i) - (4 - 5i)?

Back

The result is 6 + 13i.

Front

What is the result of (-7 + 9i) + (2 - 10i)?

Back

The result is -5 - i.

Front

What is the result of (18 - 3i) + (-2 - 5i)?

Back

The result is 16 - 8i.

Front

How do you simplify the expression (1 + 5i) + (1 - 5i)?

Back

The simplified expression is 2.

Front

What is the result of (8 + 9i) + (4 - 6i)?

Back

The result is 12 + 3i.

Front

What is the imaginary unit 'i'?

Back

The imaginary unit 'i' is defined as the square root of -1, i.e., i^2 = -1.

Front

What is the conjugate of a complex number?

Back

The conjugate of a complex number a + bi is a - bi.