Question
The Existence of Imaginary Numbers Quick Check
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Question
Which is the solution to the equation 2(x−16)2=−8, re-expressed as a complex number in the standard form a±bi?(1 point)
Responses
16±2i
16 plus or minus 2 i
−4±2i
negative 4 plus or minus 2 i
16±2i2–√
16 plus or minus 2 i Start Root 2 End Root
4±2i2–√
Answers
GPT-4o mini
To solve the equation \( 2(x - 16)^2 = -8 \), let's start by simplifying it:
1. Divide both sides by 2:
\[
(x - 16)^2 = -4
\]
2. Next, take the square root of both sides, remembering that the square root of a negative number will introduce \( i \) (the imaginary unit):
\[
x - 16 = \pm \sqrt{-4} = \pm 2i
\]
3. Now, isolate \( x \):
\[
x = 16 \pm 2i
\]
Thus, the solution in standard form \( a \pm bi \) is \( 16 \pm 2i \).
The correct response is:
- **16±2i**
- **16 plus or minus 2 i**
1. Divide both sides by 2:
\[
(x - 16)^2 = -4
\]
2. Next, take the square root of both sides, remembering that the square root of a negative number will introduce \( i \) (the imaginary unit):
\[
x - 16 = \pm \sqrt{-4} = \pm 2i
\]
3. Now, isolate \( x \):
\[
x = 16 \pm 2i
\]
Thus, the solution in standard form \( a \pm bi \) is \( 16 \pm 2i \).
The correct response is:
- **16±2i**
- **16 plus or minus 2 i**