Add, subtract, multiply, and divide complex numbers

Learning Objectives Add and subtract complex numbers by combining like terms. Multiply complex numbers using the distributive property and the identity i^2 = -1. Identify the complex conjugate of a given complex number. Divide complex numbers by multiplying the numerator and denominator by the complex conjugate. Simplify expressions involving multiple operations with complex numbers. Express all final answers in standard form (a + bi). Ever been told you can't take the square root of a negative number? 🤔 In the world of complex numbers, you can, and it opens up a whole new dimension of mathematics! This tutorial will guide you through the four basic arithmetic operations—addition, subtraction, multiplication, and division—with complex numbers. Mastering these skills i...

TermDefinitionExample Complex NumberA number that can be expressed in the form a + bi, where 'a' and 'b' are real numbers and 'i' is the imaginary unit.5 + 2i is a complex number where a=5 and b=2. Imaginary Unit (i)The imaginary unit 'i' is defined as the principal square root of -1 (i = √-1). Its most important property is that i^2 = -1.√-9 = √(9 * -1) = √9 * √-1 = 3i. Real PartIn a complex number a + bi, the real number 'a' is the real part.In the complex number 7 - 4i, the real part is 7. Imaginary PartIn a complex number a + bi, the real number 'b' is the imaginary part.In the complex number 7 - 4i, the imaginary part is -4. Standard FormThe standard form of a complex number is a + bi, where the real part comes first and the...

Addition and Subtraction (a + bi) ± (c + di) = (a ± c) + (b ± d)i To add or subtract complex numbers, combine the real parts together and the imaginary parts together, just like combining like terms in algebra. Multiplication (a + bi)(c + di) = (ac - bd) + (ad + bc)i Multiply complex numbers using the distributive property (or FOIL method), as you would with binomials. Remember to replace any instance of i^2 with -1 and simplify. Division (using the Complex Conjugate) \frac{a + bi}{c + di} = \frac{(a + bi)(c - di)}{(c + di)(c - di)} = \frac{(ac + bd) + (bc - ad)i}{c^2 + d^2} To divide complex numbers, multiply the numerator and the denominator by the complex conjugate of the denominator. This transforms the denominator into a real number, allowing you to write the re...