Operations on Complex Numbers

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

What is the imaginary unit 'i'?

Back

The imaginary unit 'i' is defined as i = √(-1). It is used to represent the square root of negative numbers.

Front

How do you multiply complex numbers?

Back

To multiply complex numbers, use the distributive property (FOIL method) and combine like terms. For example, (a + bi)(c + di) = ac + adi + bci + bdi², where i² = -1.

Front

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

Back

3 + 12i.

Front

How do you simplify powers of 'i'?

Back

Powers of 'i' cycle every four: i^1 = i, i^2 = -1, i^3 = -i, i^4 = 1. To simplify i^n, find n mod 4.

Front

What is the simplified form of i^24?

Back

1.

Front

How do you add complex numbers?

Back

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

Front

What is the result of adding (-9 + 5i) + (3 - 2i)?

Back

-6 + 3i.

Front

How do you subtract complex numbers?

Back

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

Front

What is the result of subtracting (11 - 7i) - (-3 + 12i)?

Back

14 - 19i.