Add and Subtract 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 i^2 = -1.

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

How do you subtract two complex numbers?

Back

To subtract two 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 result of (5 + 3i) + (2 + 4i)?

Back

The result is (5 + 2) + (3 + 4)i = 7 + 7i.

Front

What is the result of (6 - 2i) - (3 + 5i)?

Back

The result is (6 - 3) + (-2 - 5)i = 3 - 7i.

Front

What is the conjugate of a complex number?

Back

The conjugate of a complex number a + bi is a - bi. It reflects the number across the real axis in the complex plane.

Front

What is the modulus of a complex number?

Back

The modulus of a complex number a + bi is given by the formula |a + bi| = √(a² + b²). It represents the distance from the origin to the point (a, b) in the complex plane.

Front

Simplify: (3 + 4i) + (5 - 2i)

Back

The result is (3 + 5) + (4 - 2)i = 8 + 2i.

Front

Simplify: (7 - 3i) - (2 + 5i)

Back

The result is (7 - 2) + (-3 - 5)i = 5 - 8i.

Front

What is the result of (1 + 2i) + (3 + 4i) - (2 + 3i)?

Back

The result is (1 + 3 - 2) + (2 + 4 - 3)i = 2 + 3i.