How Do You Divide Complex Numbers Using Conjugates?

How Do You Divide Complex Numbers Using Conjugates?

Note:

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!

Keywords:

  • problem
  • divide
  • dividing
  • complex numbers
  • complex conjugate
  • conjugates

Background Tutorials

  • Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

      • What's a Dividend and What's a Divisor?What's a Dividend and What's a Divisor?

      What's a Dividend and What's a Divisor?

      When you do division problems, you need to know the vocabulary that people use to describe what number is being divided, and what number is doing the dividing. This tutorial will help you keep that vocabulary straight!

  • 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!

  • Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.

      • What's a Real Number?What's a Real Number?

      What's a Real Number?

      Real numbers are numbers that can be found on the number line. This includes both the rational and irrational numbers. This tutorial explains real numbers and gives some great examples. Take a look!

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

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 Add Complex Numbers?How Do You Add Complex Numbers?

      How Do You Add Complex Numbers?

      If you want to add complex numbers together, first regroup them so that like terms are next to one another. Then, add the like terms together, and you have your answer! To see an example, check out this tutorial.