Questions: Fill in the blanks. The imaginary unit i is defined as i= where i^2= .

Transcript text: Fill in the blanks. The imaginary unit $i$ is defined-as $i=$ $\qquad$ where $i^{2}=$ $\qquad$ .

Solution

Solution Steps

Step 1: Define the Imaginary Unit

The imaginary unit $i$ is defined as $i = \sqrt{-1}$, which is a fundamental concept in complex numbers.

Step 2: State the Fundamental Property of the Imaginary Unit

By its fundamental property, $i^2 = -1$, which differentiates imaginary numbers from real numbers.

Final Answer:

The imaginary unit $i$ is defined as $i = \sqrt{-1}$, where $i^2 = -1$. This definition and property are crucial for understanding and working with complex numbers.

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