/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 18 \((15+8 i)+(2+4 i)\)... [FREE SOLUTION] | 91影视

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Chapter 9: Problem 18

\((15+8 i)+(2+4 i)\)

Short Answer

Expert verified
17 + 12i

Step by step solution

01

Identify the real and imaginary parts

The given complex numbers are \(15 + 8i\) and \(2 + 4i\). Identify the real and imaginary parts of each. Here, 15 and 2 are the real parts, while 8i and 4i are the imaginary parts.
02

Add the real parts together

Add the real parts of the complex numbers: \(15 + 2\). This gives \(17\).
03

Add the imaginary parts together

Add the imaginary parts of the complex numbers: \(8i + 4i\). This gives \(12i\).
04

Combine the results

Combine the sum of the real parts and the sum of the imaginary parts: \(17 + 12i\). This is the final answer.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

real and imaginary parts
Complex numbers are numbers that have a real part and an imaginary part. The real part is a regular number, like the ones we're used to dealing with, while the imaginary part has an 'i' next to it. The 'i' stands for the square root of -1.

In our example, the complex numbers are \(15 + 8i\) and \(2 + 4i\). Here:
  • The real parts are 15 and 2.
  • The imaginary parts are 8i and 4i.
Recognizing and separating these parts is the first step to performing operations like addition on complex numbers.

Always start by identifying the real and imaginary parts.
adding real parts
To add complex numbers, you start by adding the real parts together. Think of it like adding two regular numbers.

For example:
From our exercise, we need to add the real parts of \(15 + 8i\) and \(2 + 4i\).

The real parts are 15 and 2.

When we add them together, we get: \(15 + 2 = 17\).

This result is the real part of our final answer.

Remember: You are only working with the numbers without the 'i' here.
adding imaginary parts
Next, we add the imaginary parts. Just like with real parts, treat the imaginary parts separately, focusing on the coefficients of 'i'.

For our exercise:
We need to add the imaginary parts of \(15 + 8i\) and \(2 + 4i\).

The imaginary parts are 8i and 4i.

When we add them together, we get: \(8i + 4i = 12i\).

This gives us the imaginary part of our final answer.

Finally, combine the sums of the real and imaginary parts: \(17 + 12i\). That鈥檚 your answer!

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