Complex Number Test Review

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

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 value of i^2?

Back

i^2 = -1.

Front

How do you simplify √-x?

Back

√-x = i√x, where x is a positive real number.

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 two complex numbers (a + bi) and (c + di)?

Back

To add two complex numbers, combine the real parts and the imaginary parts: (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 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).