Table of Contents

- 1 What are the steps to simplify complex numbers?
- 2 What is the product of complex numbers (- 3i 4 and 3i 4?
- 3 What is the modulus of the complex number − 4 3i?
- 4 How do you find the product of a complex number and its conjugate?
- 5 What is the modulus of the complex number i 2 n 1 )(- i 2n 1 where n in N and i sqrt (- 1?
- 6 What is the multiplicative inverse of √ 5 3i?
- 7 How do you multiply two complex numbers?
- 8 How do you use the simple simplify calculator?
- 9 What is the square root of a complex number (a+bi)?

## What are the steps to simplify complex numbers?

- Step 1: Multiply the complex numbers in the same manner as polynomials.
- Step 2: Simplify the expression.
- Step 3: Write the final answer in standard form.
- Step 1: Multiply the complex numbers in the same manner as polynomials.
- Step 2: Simplify the expression.
- Step 3: Write the final answer in standard form.

### What is the product of complex numbers (- 3i 4 and 3i 4?

The product of the complex numbers (-3i + 4) and (3i + 4) is 25.

#### What is the modulus of the complex number − 4 3i?

5

The complex number z =4+3i. To summarise, the modulus of z =4+3i is 5 and its argument is θ = 36.97◦.

**How do you simplify complex arithmetic?**

To add two or more complex numbers, first just add the real portions of the numbers together. For example, to simplify the sum of (a+bi) and (c+di), first identify that a and c are the real number portions, and add them together. Symbolically, this will be (a+c).

**What is the sum of the complex numbers 2 3i and 4 8i where i =- 1?**

The sum of two complex numbers, a + bi and c + di, is found by adding real parts and imaginary parts, respectively, that is, (a + bi) + (c + di) = (a + c) + (b + d)i. Therefore, the sum of 2 + 3i and 4 + 8i is (2 + 4) + (3 + 8)i = 6 + 11i.

## How do you find the product of a complex number and its conjugate?

For a complex number a + bi, the conjugate is a – bi.

- For 2 – 3i, the conjugate is 2 – (-3i) = 2 + 3i. (2-3i)(2+3i) = 4 + 6i – 6i – 9i2 = 4 + 9 = 13 [Use the FOIL method] Note that the product is always a real number.
- For -3 + 4i, the conjugate is -3 – 4i. (-3+4i)(-3-4i) = __________
- Can you do #3 on your own?

### What is the modulus of the complex number i 2 n 1 )(- i 2n 1 where n in N and i sqrt (- 1?

Hence the modulus of the complex number i2n + 1(-i)2n – 1 is 1.

#### What is the multiplicative inverse of √ 5 3i?

Thus, the multiplicative inverse of $\sqrt 5 + 3i$ is $\dfrac{1}{{14}}\left( {\sqrt 5 – 3i} \right)$(in simplified form).

**How do you simplify complex fractions?**

How to simplify complex fractions

- Convert mixed numbers to improper fractions.
- Reduce all fractions when possible.
- Find the least common denominator (LCD) of all fractions appearing within the complex fraction.
- Multiply both the numerator and the denominator of the complex fraction by the LCD.

**How to simplify complex expressions with i2 = -1?**

And use definition i2 = -1 to simplify complex expressions. Many operations are the same as operations with two-dimensional vectors. To multiply two complex numbers, use distributive law, avoid binomials, and apply i2 = -1.

## How do you multiply two complex numbers?

To multiply two complex numbers, use distributive law, avoid binomials, and apply i2 = -1. The division of two complex numbers can be accomplished by multiplying the numerator and denominator by the denominator’s complex conjugate. This approach avoids imaginary unit i from the denominator.

### How do you use the simple simplify calculator?

Simplify Calculator. Enter the expression you want to simplify into the editor. The simplification calculator allows you to take a simple or complex expression and simplify and reduce the expression to it’s simplest form. The calculator works for both numbers and expressions containing variables.

#### What is the square root of a complex number (a+bi)?

Square root of complex number (a+bi) is z, if z 2 = (a+bi). Here ends simplicity. Because of the fundamental theorem of algebra, you will always have two different square roots for a given number.