Re express 3 √-32 as a complex number with the imaginary unit i= √-1
To convert √-32 into a complex number, we can write it as √(-1) * √32.
The square root of -1 is defined as i, so we can rewrite the expression as i * √32.
Now we can simplify √32. The square root of 32 can be broken down into the product of the square root of 16 and the square root of 2. Simplifying further, the square root of 16 is 4, so we have 4 * √2.
Putting it all together, we have i * √32 = i * 4 * √2.
This can be further simplified as 4i√2, which is the complex number representation of √-32.
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To express √(-32) as a complex number, we can rewrite it as √(32) * √(-1).
The square root of 32 can be simplified as √(16 * 2), which becomes 4√2.
Now, the square root of -1 is defined as the imaginary unit i, so √(-1) can be expressed as i.
Putting it all together, √(-32) can be written as 4√2 * i, which is the complex number representation of √(-32).
To express √-32 as a complex number with the imaginary unit i = √-1, we need to simplify the square root of -32. Here's how you can do it:
Step 1: Factor out the perfect squares from -32.
-32 can be written as -1 * 2^5.
Step 2: Rewrite in terms of the imaginary unit.
Since we know that i = √-1, we can express the square root of -32 as √(-1 * 2^5).
Step 3: Simplify the expression.
√(-1 * 2^5) can be rewritten as √(-1) * √(2^5) = i * 2√2^5.
Step 4: Further simplify the expression and calculate the value.
2√2^5 is equal to 2 * 2^2 * √2 = 4 * 2√2 = 8√2.
Therefore, √-32 can be expressed as 8√2i in terms of the imaginary unit i.