Math Problem Statement

Which expression is equivalent to (7 + 4i) + (8 + i)?

Solution

Let's solve the expression given in the image:

We are asked which expression is equivalent to (7+4i)+(8+i)(7 + 4i) + (8 + i).

To simplify this:

  1. Combine the real parts: 7+8=157 + 8 = 15.
  2. Combine the imaginary parts: 4i+i=5i4i + i = 5i.

Thus, the expression simplifies to 15+5i15 + 5i.

So, the correct answer is:

15 + 5i

Let me know if you need more details or have any other questions!

Here are some related questions:

  1. How do you add complex numbers?
  2. What is the difference between real and imaginary numbers?
  3. How do you subtract complex numbers?
  4. What is the conjugate of a complex number?
  5. What is the modulus of a complex number?

Tip: When adding or subtracting complex numbers, always group real parts and imaginary parts separately!

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Math Problem Analysis

Mathematical Concepts

Complex Numbers
Addition of Complex Numbers

Formulas

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

Theorems

Addition of Complex Numbers

Suitable Grade Level

Grades 7-9