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

How do you add two complex numbers?

Back

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

Front

How do you subtract two complex numbers?

Back

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

Front

What is the product of two complex numbers (a + bi) and (c + di)?

Back

The product is given by (a + bi)(c + di) = ac + adi + bci + bdi^2 = (ac - bd) + (ad + bc)i.

Front

What is the value of i^2?

Back

i^2 = -1.

Front

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

Back

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

Front

How do you multiply a complex number by its conjugate?

Back

Multiplying a complex number a + bi by its conjugate a - bi gives (a + bi)(a - bi) = a^2 + b^2.

Front

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

Back

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

Front

What does it mean for a complex number to be purely imaginary?

Back

A complex number is purely imaginary if its real part is zero, i.e., it can be expressed as 0 + bi.

Front

What is the real part of the complex number 3 + 4i?

Back

The real part is 3.