Chapter 4, Problem 1RE

To determine

To calculate: The standard form of the provided expression $6+\sqrt{-4}$.

Answer to Problem 1RE

The standard form of complex number of the provided expression $6+\sqrt{-4}$ is $6+2i$.

Explanation of Solution

Calculation:

Consider the provided expression,

$6+\sqrt{-4}$

Simplify the provided equation,

$\begin{array}{c}6+\sqrt{-4}=6+\sqrt{4\left(-1\right)}\\ =6+\left(2\sqrt{-1}\right)\end{array}$

The standard form of complex number is represented as $a+bi$, where $a$ is the real part of the complex number, $b$ is the imaginary part of the complex number and $i$ is the imaginary unit whose value is $\sqrt{-1}$.

Substitute $i=\sqrt{-1}$ in the above equation,

$6+\sqrt{-4}=6+2i$

Hence, the standard form of the provided expression $6+\sqrt{-4}$ is $6+2i$.