Adding and Subtracting Complex Numbers and Powers of i

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

What is the imaginary unit 'i'?

Back

Front

How do you add complex numbers?

Back

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

Front

How do you subtract 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

What is the result of (3 + i) + (-8 + 6i)?

Back

The result is -5 + 7i.

Front

What is the result of (8 + 7i) - (6 + 3i)?

Back

The result is 2 + 4i.

Front

What is the result of (10 + 15i) - (48 - 30i)?

Back

The result is -38 + 45i.

Front

What is the result of (7 + 2i) - (-12 - 4i)?

Back

The result is 19 + 6i.

Front

What is the result of (4 - 7i) - (-3 + 6i)?

Back

The result is 7 - 13i.

Front

What is the conjugate of a complex number a + bi?

Back

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