https://file.aiquickdraw.com/mathbot/file/1727037107371aeev0znd.jpg

The equation shown in the image is:

\[
\sqrt{2} - 5i + y = 0
\]

To solve for \( y \), we can isolate it on one side of the equation:

\[
y = -(\sqrt{2} - 5i)
\]

Thus,

\[
y = -\sqrt{2} + 5i
\]

So, the solution for \( y \) is:

\[
y = -\sqrt{2} + 5i
\]

Would you like further details on this, or have any additional questions?

Here are five related questions you might explore:
1. How do we handle complex numbers in equations like this?
2. What are the properties of the imaginary unit \( i \)?
3. How do we solve similar equations with real and imaginary parts?
4. What is the meaning of the square root of 2 in different mathematical contexts?
5. How do we graph complex numbers on the complex plane?

**Tip:** When solving equations involving complex numbers, always remember to treat real and imaginary parts separately when simplifying.

Learn how to solve for y in the equation √2 - 5i + y = 0, which includes the use of imaginary numbers and algebraic manipulation. Suitable for students in Grades 9-12.

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