Complex Numbers: Definitions + Simple Ops (Add, Subtract, Mult)

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 does the imaginary unit 'i' represent?

Back

The imaginary unit 'i' represents the square root of -1, i.e., i = √-1.

Front

What is the value of i^2?

Back

i^2 = -1.

Front

How do you add two complex numbers, (a + bi) and (c + di)?

Back

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

Front

How do you subtract two complex numbers, (a + bi) and (c + di)?

Back

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

Front

How do you multiply two complex numbers, (a + bi) and (c + di)?

Back

To multiply two complex numbers, use the distributive property: (a + bi)(c + di) = ac + adi + bci + bdi^2 = (ac - bd) + (ad + bc)i.

Front

What is the result of (3i)(5i)?

Back

(3i)(5i) = 15i^2 = 15(-1) = -15.

Front

How do you write a complex number in standard form?

Back

A complex number is written in standard form as a + bi, where a is the real part and b is the imaginary part.

Front

What is the conjugate of a complex number a + bi?

Back

The conjugate of a complex number a + bi is a - bi.

Front

What is the modulus of a complex number a + bi?

Back

The modulus of a complex number a + bi is given by |a + bi| = √(a^2 + b^2).