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Chapter 1: Problem 5

Add or subtract as indicated and write the result in standard form. $$ 6-(-5+4 i)-(-13-i) $$

Short Answer

Expert verified
The simplified form of the given expression in standard form is \(24 - 3i\).

Step by step solution

01

Understanding and simplifying the given expression

The given expression is \(6 - (-5+4i) - (-13-i)\). To simplify this expression, it is crucial to handle negative signs correctly. The expression can be rewritten as \(6 + (5-4i) + (13+i)\) following the rules of changing the sign of both the real and imaginary components of complex numbers when they are proceeded by a negative sign.
02

Adding Real Parts and Imaginary Parts Separately

The general rule for the addition of complex numbers is to add real parts together and imaginary parts together separately. The expression will therefore be simplified as follows: Real Parts: 6 + 5 + 13 = 24. Imaginary Parts: -4i + i = -3i.
03

Write in standard form

The complex number is written in the standard form of a + bi where 'a' is the real part, and 'bi' is the imaginary part. In our case, a = 24 and bi = -3i. So, the final answer will be written in standard form as: 24 - 3i.

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