Find the square root of 7+24i

Explanation

To find the square root of the complex number \( 7 + 24i \), we can express the square root in the form \( x + yi \), where \( x \) and \( y \) are real numbers. We will follow these steps:

### Step 1: Set up the equation
Let \( \sqrt{7 + 24i} = x + yi \).

### Step 2: Square both sides
Squaring both sides gives:
\[
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