Questions: Express √(-36) - √(-100) as a complex number (in terms of i ): √(-36) - √(-100) =

Transcript text: Express $\sqrt{-36}-\sqrt{-100}$ as a complex number (in terms of $i$ ): \[ \sqrt{-36}-\sqrt{-100}= \]

Solution

Solution Steps

To express $\sqrt{-36} - \sqrt{-100}$ as a complex number, we recognize that the square root of a negative number involves the imaginary unit $i$, where $i = \sqrt{-1}$. Thus, $\sqrt{-36} = \sqrt{36} \cdot i$ and $\sqrt{-100} = \sqrt{100} \cdot i$. Calculate these square roots and subtract them.

Step 1: Identify the Imaginary Components

To express $\sqrt{-36}$ and $\sqrt{-100}$ as complex numbers, we use the property that $\sqrt{-a} = \sqrt{a} \cdot i$.

\[ \sqrt{-36} = \sqrt{36} \cdot i = 6i \]

\[ \sqrt{-100} = \sqrt{100} \cdot i = 10i \]

Step 2: Subtract the Complex Numbers

Subtract the two complex numbers:

\[ 6i - 10i = (6 - 10)i = -4i \]