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Chapter 1: Problem 3

Add or subtract as indicated and write the result in standard form. $$ (3+2 i)-(5-7 i) $$

Short Answer

Expert verified
The result in the standard form is \(-2 + 9i\).

Step by step solution

01

Identify the Real and Imaginary Parts

To perform this operation, first, recognize the real and imaginary parts of both complex numbers. Here, for the complex number \(3+2i\), 3 is the real part and 2 is the imaginary part. For the complex number \(5-7i\), 5 is the real part and -7 is the imaginary part.
02

Subtract Real Parts

Subtract the real part of the second complex number from the real part of the first complex number. Here, that would be \(3 (from 3+2i) - 5 (from 5-7i) = -2 \).
03

Subtract Imaginary Parts

Subtract the imaginary part of the second complex number from the imaginary part of the first complex number. Here, that would be \(2 (from 3+2i) - (-7) (as the second imaginary part is negative, so the operation becomes addition) = 9\).
04

Write in Standard Form

Combine the real and imaginary parts that have been obtained to form the standard form of a complex number which is a + bi. In this case, the result is \(-2 + 9i \).

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