How Do You Multiply Complex Numbers Using FOIL?

How Do You Multiply Complex Numbers Using FOIL?

Note:

Get some practice multiplying complex numbers together using the FOIL method! This tutorial takes you through the process of multiplying two complex numbers together.

Keywords:

  • problem
  • multiply
  • complex numbers
  • i
  • foil
  • distributive property

Background Tutorials

  • Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).

      • What is a Variable?What is a Variable?

      What is a Variable?

      You can't do algebra without working with variables, but variables can be confusing. If you've ever wondered what variables are, then this tutorial is for you!

      • What is the Substitution Property of Equality?What is the Substitution Property of Equality?

      What is the Substitution Property of Equality?

      If you ever plug a value in for a variable into an expression or equation, you're using the Substitution Property of Equality. This property allows you to substitute quantities for each other into an expression as long as those quantities are equal. Watch this tutorial to learn about this useful property!

  • Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

      • What are Like Terms?What are Like Terms?

      What are Like Terms?

      Combining like terms together is a key part of simplifying mathematical expressions, so check out this tutorial to see how you can easily pick out like terms from an expression

  • Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.

      • What is a Polynomial?What is a Polynomial?

      What is a Polynomial?

      If you learn about algebra, then you'll see polynomials everywhere! In this tutorial, you'll learn the definition of a polynomial and see some of the common names for certain polynomials.

      • What's FOIL?What's FOIL?

      What's FOIL?

      The FOIL method. No, not aluminum foil! The FOIL method stands for First, Outer, Inner, and Last. It's a popular way multiply two binomials together. This tutorial makes the FOIL method a breeze!

Further Exploration

  • Use the relation i^2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

      • How Do You Find Higher Powers of i?How Do You Find Higher Powers of i?

      How Do You Find Higher Powers of i?

      When the imaginary number 'i' has a large exponent, it can take a while to simplify it. Luckily, this tutorial gives you a trick to quickly find a higher power of 'i'!

  • Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.

      • How Do You Divide Complex Numbers Using Conjugates?How Do You Divide Complex Numbers Using Conjugates?

      How Do You Divide Complex Numbers Using Conjugates?

      To divide complex numbers, you usually need to multiply by the complex conjugate of the denominator. Follow along with this tutorial to see how to find that complex conjugate and multiply with it to perform the division!