Complex Numbers (Add & Subtract)

Front

Define 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 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

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

Simplify: (10 + 15i) - (48 - 30i)

Back

-38 + 45i

Front

What is the result of adding (5 - 2i) + (-7 + 8i)?

Back

-2 + 6i

Front

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

Back

-9i

Front

How do you multiply a complex number by 'i'?

Back

Multiplying a complex number by 'i' rotates the number 90 degrees counterclockwise in the complex plane. For example, i(a + bi) = -b + ai.

Front

Simplify: 2√-32

Back

8i√2

Front

What is the result of adding 2i + 3 + 7 - 12i?

Back

-10i + 10