QuestionFind the real and imaginary parts of the complex number $9-\sqrt{-2}$ .

Studdy Solution

STEP 1

Assumptions1. We are given a complex number in the form $a + bi$ , where $a$ is the real part and $b$ is the imaginary part. . The given complex number is $9 - \sqrt{-}$ .

STEP 2

We need to express the complex number in the form $a + bi$ . To do this, we need to simplify the square root of a negative number.
The square root of a negative number can be expressed as $i$ times the square root of the positive of that number. This is because $i$ is defined as $\sqrt{-1}$ .
So, $\sqrt{-2} = i\sqrt{2}$ .

STEP 3

Substitute $i\sqrt{2}$ for $\sqrt{-2}$ in the given complex number.
$9 - \sqrt{-2} =9 - i\sqrt{2}$

STEP 4

Now, the complex number is in the form $a + bi$ . We can identify the real and imaginary parts.
The real part is the coefficient of the term without $i$ , which is $9$ .
The imaginary part is the coefficient of the term with $i$ , which is $-\sqrt{2}$ .
So, the real part is $9$ and the imaginary part is $-\sqrt{2}$ .

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