Question

For the complex number $\sqrt {37} + \sqrt { - 19}$ . Real part is $\sqrt {37}$ and the imaginary part is $\sqrt {19}$ . Enter 1 if true or 0 for false.

Answer 1

Here we need to check whether the real part and the imaginary part of the complex number. We know that the complex number is defined as a number which is a combination of both the real number and the imaginary number. We will first write the given complex number in the standard form and then using the property of the complex number, we will find the answer.

Complete step-by-step answer:
The given complex number is $\sqrt {37} + \sqrt { - 19}$.
We know that the complex number consists of both the real number and the imaginary number. It is written as $a + ib$ where, $a$ is the real part and $b$ is the imaginary part.
So, we will first write the given complex number i.e. $\sqrt {37} + \sqrt { - 19}$ in the standard form.
We can write the complex number as
$\sqrt {37} + \sqrt { - 19} = \sqrt {37} + \sqrt { - 1} \times \sqrt {19}$
We know that $i = \sqrt { - 1}$.
Substituting this value in the above equation, we get
$\Rightarrow \sqrt {37} + \sqrt { - 19} = \sqrt {37} + i\sqrt {19}$
On comparing the complex number with the standard form, we get
Real part is $\sqrt {37}$ and the imaginary part is $\sqrt {19}$ .
Therefore, the given statement is correct and so we will enter 1 for this..

Note: Here, the imaginary part is written with the sign $i$. When we add or subtract two complex numbers, we add or subtract the real part of the first complex number with the real part of the second complex number and add or subtract the imaginary part of the first complex number with the imaginary part of the second complex number.