## How is multiplying complex numbers different than multiplying polynomials?

Multiplying complex numbers is much like multiplying binomials. The major difference is that we work with the real and imaginary parts separately.

**How are complex numbers related to polynomials?**

The factors that are first-degree polynomials are real roots of the original polynomial. Therefore, whenever a complex number is a root of a polynomial with real coefficients, its complex conjugate is also a root of that polynomial. As an example, we’ll find the roots of the polynomial x5 – x4 + x3 – x2 – 12x + 12.

**What does multiplying by a complex number do?**

Multiplying a complex number by a real number (x + yi) u = xu + yu i. In other words, you just multiply both parts of the complex number by the real number. For example, 2 times 3 + i is just 6 + 2i. Similarly, when you multiply a complex number z by 1/2, the result will be half way between 0 and z.

### How do you multiply and divide a complex number?

We first write the division as a fraction, then find the complex conjugate of the denominator, and multiply. Multiply the numerator and denominator by the complex conjugate of the denominator. Apply the distributive property. = −1. \\displaystyle a-bi a − bi. It is found by changing the sign of the imaginary part of the complex number.

**Why are complex numbers more complicated than addition and multiplication?**

\\displaystyle \\left (3 – 4iight)\\left (2+3iight) (3 − 4i)(2 + 3i). Division of two complex numbers is more complicated than addition, subtraction, and multiplication because we cannot divide by an imaginary number, meaning that any fraction must have a real-number denominator.

**What’s the difference between multiplying binomials and complex numbers?**

Multiplying complex numbers is much like multiplying binomials. The major difference is that we work with the real and imaginary parts separately. Let’s begin by multiplying a complex number by a real number. We distribute the real number just as we would with a binomial. So, for example,

## Which is an example of a complex number?

A Complex Number is a combination of a Real Number and an Imaginary Number: A Real Number is the type of number we use every day. Examples: 12.38, ½, 0, −2000. An Imaginary Number, when squared gives a negative result: The “unit” imaginary number when squared equals −1.