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Chapter 1: Problem 4

Add or subtract as indicated and write the result in standard form. $$ (-7+5 i)-(-9-11 i) $$

Short Answer

Expert verified
The result of the addition and subtraction of the given complex numbers in standard form is \(2 + 16i\)

Step by step solution

01

Identify the Real and Imaginary Parts

The given expression is \( (-7+5i)-(-9-11i) \). Here, the real part of the first complex number is -7 and the imaginary part is 5i. In the second complex number, -9 is the real part and -11i is the imaginary part.
02

Simplify the Expression

We can rewrite the expression as \( (-7+5i) + (9+11i) \) because subtraction is the same as adding the negative. Next, group the real parts and the imaginary parts as follows, \( (-7+9)+(5i+11i) \)
03

Add Real and Imaginary Parts

Add the real parts together: \(-7 + 9 = 2\), and add the imaginary parts together: \(5i + 11i = 16i \)
04

Write the Result in Standard Form

Combine the real and imaginary parts to get the final answer in standard form of a complex number, \(a + bi\). So the final result is \( 2 + 16i \)

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