Complex Number Calculations

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

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

What is the imaginary unit 'i'?

Back

The imaginary unit 'i' is defined as the square root of -1. It is used to extend the real number system to include solutions to equations that do not have real solutions.

Front

What is the result of adding (8i) and (-3 - 4i)?

Back

-3 + 4i.

Front

What is the result of adding (3 + 4i) and (5 - 2i)?

Back

8 + 2i.

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 subtracting (5 + 3i) - (2i)?

Back

5 + i.

Front

What is the result of adding (-7 + 6i) and (3 + 2i)?

Back

-4 + 8i.

Front

What is the result of adding (9 - 7i) and (-6 + 14i)?

Back

3 + 7i.

Front

What is the conjugate of a complex number?

Back

The conjugate of a complex number a + bi is a - bi. It is obtained by changing the sign of the imaginary part.