Math Problem Statement

Add (5 - 2i) + (3 + 3i) and write the result in standard form.

Solution

Let's break down the addition of the two complex numbers shown in the image:

(52i)+(3+3i)(5 - 2i) + (3 + 3i)

To add these, we combine the real parts and the imaginary parts separately:

  1. Real part: 5+3=85 + 3 = 8
  2. Imaginary part: 2i+3i=i-2i + 3i = i

So the result of the addition is:

8+i8 + i

This is already in standard form, which is a+bia + bi, where aa is the real part and bb is the coefficient of the imaginary part ii.

Would you like any further details or clarifications?

Here are 5 related questions:

  1. How do you subtract two complex numbers?
  2. What happens when you multiply two complex numbers?
  3. How do you find the magnitude of a complex number?
  4. How is the complex conjugate of a number calculated?
  5. How would you divide two complex numbers?

Tip: Always remember that in complex numbers, real and imaginary parts are treated separately during basic operations like addition and subtraction.

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Math Problem Analysis

Mathematical Concepts

Complex Numbers
Addition

Formulas

(a + bi) + (c + di) = (a + c) + (b + d)i

Theorems

Basic Operations on Complex Numbers

Suitable Grade Level

Grades 9-12