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 i = √(-1).

Front

What is the imaginary unit 'i'?

Back

The imaginary unit 'i' is defined as the square root of -1, i.e., i = √(-1). It is used to extend the real number system to complex numbers.

Front

What is the result of i^2?

Back

i^2 = -1.

Front

What is the result of i^3?

Back

i^3 = i^2 * i = -1 * i = -i.

Front

What is the result of i^4?

Back

i^4 = (i^2)^2 = (-1)^2 = 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

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 simplified form of (3 + 4i) + (2 - 3i)?

Back

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

Front

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

Back

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

Front

What is the result of i^5?

Back

i^5 = i^4 * i = 1 * i = i.