Question

Select all the complex numbers in the given table

Answer 1

The complex number from the table are

$1+\sqrt{-3}, \ 4-3 \sqrt{-16}, \ \frac{3+2 \sqrt{-9}}{7}, \ 9 \sqrt{-\frac{7}{5}}$

Solution:

Let us solve and identify the complex number.

(A) $5-\sqrt{\frac{9}{4}}$

$5-\sqrt{\frac{9}{4}}= 5-\sqrt{\frac{3^2}{2^2}}$

            $= 5-\frac{3}{2}$

           = 3.5

This is not a complex number.

(B) $1+\sqrt{-3}$

$1+\sqrt{-3}=1+\sqrt{-1\times 3}$

We know that $\sqrt{-1} =i$.

$1+\sqrt{-3}=1+\sqrt{3}i$

This is a complex number.

(C) $4-3 \sqrt{-16}$

$4-3 \sqrt{-16}=4-3 \sqrt{-1\times 4^2}$

$4-3 \sqrt{-16}=4-3\times4 \sqrt{-1}$

We know that $\sqrt{-1} =i$.

$4-3 \sqrt{-16}=4-12i$

This is a complex number.

(D) $\frac{2-\sqrt{12}}{5}$

$\frac{2-\sqrt{12}}{5}=\frac{2-2\sqrt{3}}{5}$

There is no –1 in the root.

This is not a complex number.

(E) $\frac{3+2 \sqrt{-9}}{7}$

$\frac{3+2 \sqrt{-9}}{7}=\frac{3+2 \sqrt{-1\times 3^2}}{7}$    

We know that $\sqrt{-1} =i$.  

             $=\frac{3+6i}{7}$

This is a complex number.

(F) $9 \sqrt{-\frac{7}{5}}$

$9 \sqrt{-\frac{7}{5}}=9 \sqrt{-1 \times \frac{7}{5}}$

We know that $\sqrt{-1} =i$.  

$9 \sqrt{-\frac{7}{5}}=9 \sqrt{ \frac{7}{5}}i$

This is a complex number.

Hence the complex number from the table are

$1+\sqrt{-3}, \ 4-3 \sqrt{-16}, \ \frac{3+2 \sqrt{-9}}{7}, \ 9 \sqrt{-\frac{7}{5}}$