# How do multiplication and division work with complex numbers?

## How do multiplication and division work with complex numbers?

How To: Given two complex numbers, divide one by the other. Write the division problem as a fraction. Determine the complex conjugate of the denominator. Multiply the numerator and denominator of the fraction by the complex conjugate of the denominator.

How do you solve complex division equations?

Steps for Dividing Complex Numbers Multiply the conjugate with the numerator and the denominator of the complex fraction. Apply the algebraic identity (a+b)(a-b)=a2 – b2 in the denominator and substitute i2 = -1. Apply the distributive property in the numerator and simplify.

### What is multiplication of radicals?

To multiply two radicals together, you can first rewrite the problem as one radical. The two numbers inside the square roots can be multiplied together under one square root. Simplify what’s inside the radical to write your final answer.

What happens when a complex number is multiplied by i?

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.

#### How do you multiply and divide radicals?

Find the LCM (lowest common multiple) of the indices. To find the LCM of the indexes,find the smallest number that is evenly divisible by both indices.

• Write each expression with the new LCM as the index.
• Find the number that you would need to multiply each original index by to find the LCM.
• What are the rules for multiplying radicals?

– Find a perfect square factor for 24. – Break it down as a product of square roots. – Simplify the square root of 4.