Question

Rewrite the expression 4+5)}" alt="\sqrt{16-(4)(5)}" align="absmiddle" class="latex-formula">/2 as a complex number in standard form,a+bi .

Answer 1

Answer:

$2+i$

Step-by-step explanation:

Given the expression:

$\dfrac{4+\sqrt{16-(4)(5)}}{2}$

To find:

The expression of above complex number in standard form $a+bi$.

Solution:

First of all, learn the concept of $i$ (pronounced as iota) which is used to represent the complex numbers. Especially the imaginary part of the complex number is represented by $i$.

Value of $i =\sqrt{-1}$.

Now, let us consider the given expression:

$\dfrac{4+\sqrt{16-(4)(5)}}{2}\\\Rightarrow \dfrac{4+\sqrt{16-(4\times 5)}}{2}\\\Rightarrow \dfrac{4+\sqrt{16-20}}{2}\\\Rightarrow \dfrac{4+\sqrt{-4}}{2}\\\Rightarrow \dfrac{4+\sqrt{(-1)(4)}}{2}\\\Rightarrow \dfrac{4+\sqrt{(-1)}\sqrt4}{2}\\\Rightarrow \dfrac{4+\sqrt4i}{2} \ \ \ \ \ (\because \sqrt{-1} =i) \\\Rightarrow \dfrac{4+2i}{2}\\\Rightarrow 2+i$

So, the given expression in standard form is $2+i$.

Let us compare with standard form $a+bi$ so we get $a =2, b =1$.

$\therefore$ The standard form of

$\dfrac{4+\sqrt{16-(4)(5)}}{2}$

is: $\bold{2+i}$