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, combine 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 adding (2 + 3i) and (4 + 5i)?

Back

(2 + 3i) + (4 + 5i) = (2 + 4) + (3 + 5)i = 6 + 8i.

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 (3 + 2i) from (5 + 4i)?

Back

(5 + 4i) - (3 + 2i) = (5 - 3) + (4 - 2)i = 2 + 2i.

Front

What is the imaginary unit 'i'?

Back

The imaginary unit 'i' is defined as the square root of -1, which is used to extend the real number system to complex numbers.

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.

Front

How do you find the sum of (-2 + 7i) and (5 - 3i)?

Back

(-2 + 7i) + (5 - 3i) = (-2 + 5) + (7 - 3)i = 3 + 4i.

Front

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

Back

(3 + 2i) + (4 - 5i) = (3 + 4) + (2 - 5)i = 7 - 3i.

Front

What is the result of (7 - 2i) - (-4 + 3i)?

Back

(7 - 2i) - (-4 + 3i) = (7 + 4) + (-2 - 3)i = 11 - 5i.