Add and Subtract Complex Numbers

Front

Define complex numbers.

Back

Complex numbers are numbers that have a real part and an imaginary part, expressed in the form a + bi, where a is the real part, b is the imaginary part, and i is the imaginary unit, defined as i = √(-1).

Front

What is the formula for adding complex numbers?

Back

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

Front

What is the formula for subtracting complex numbers?

Back

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

Front

Calculate: (4 - 7i) - (-3 + 6i)

Back

7 - 13i

Front

Find the difference: (6 - 8i) - (1 - 3i)

Back

5 - 5i

Front

Simplify: (5 - 2i) + (-7 + 8i)

Back

-2 + 6i

Front

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

Back

7 - 3i

Front

What is the imaginary unit i?

Back

The imaginary unit i is defined as the square root of -1, i.e., i = √(-1).

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 multiply complex numbers?

Back

To multiply complex numbers (a + bi) and (c + di), use the distributive property: (ac - bd) + (ad + bc)i.