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 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

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

Back

-4 + 8i.

Front

How do you multiply complex numbers?

Back

To multiply complex numbers, use the distributive property (FOIL method) and apply the fact that i^2 = -1. For example, (a + bi)(c + di) = ac + adi + bci + bdi^2.

Front

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

Back

8 - 1i.

Front

What is the imaginary unit 'i'?

Back

The imaginary unit 'i' is defined as the square root of -1, which means i^2 = -1.

Front

What happens when you multiply two imaginary numbers?

Back

When you multiply two imaginary numbers, the result is a real number. For example, (ai)(bi) = ab(i^2) = -ab.

Front

What is the result of multiplying (3i) and (4i)?

Back

-12.

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 adding (8i) and (-3 - 4i)?

Back

-3 + 4i.