Mckenzie Pena
01/25/2023 · Senior High School
Factor the expression over the complex numbers. \( y^{2}+49 \) Enter your answer in the box.
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Tutor-Verified Answer
Step-by-step Solution
To factor the expression \( y^2 + 49 \) over the complex numbers, we can recognize that it can be expressed as a sum of squares. Specifically, we can rewrite \( 49 \) as \( 7^2 \):
\[
y^2 + 49 = y^2 + 7^2
\]
Using the formula for the sum of squares, \( a^2 + b^2 = (a + bi)(a - bi) \), where \( i \) is the imaginary unit, we can factor the expression:
Let \( a = y \) and \( b = 7 \):
\[
y^2 + 7^2 = (y + 7i)(y - 7i)
\]
Thus, the factored form of \( y^2 + 49 \) over the complex numbers is:
\[
\boxed{(y + 7i)(y - 7i)}
\]
Quick Answer
\((y + 7i)(y - 7i)\)
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