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Chapter 1: Problem 2

Add or subtract as indicated and write the result in standard form. $$ (-2+6 i)+(4-i) $$

Short Answer

Expert verified
The sum of the given complex numbers in standard form is \(2+5i\).

Step by step solution

01

Identify the Real and Imaginary Parts

First, identify the real and imaginary parts of each complex number. Here, for the first complex number (-2+6i), the real part is -2 and the imaginary part is +6. For the second complex number (4-i), the real part is 4 and the imaginary part is -1.
02

Add the Real Parts

Next, add the real parts of the two complex numbers. So, -2 (from the first number) + 4 (from the second number) = 2.
03

Add the Imaginary Parts

Then, add the imaginary parts of the two complex numbers. So, +6 (from the first number) + (-1) (from the second number) = 5.
04

Write the Result in Standard Form

Finally, write the result in standard form, \(a+bi\). In this case, the result is 2+5i. This is the standard form of the sum of the given two complex numbers.

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