Question

Drag the labels to the correct locations. Each label can be used more than once, but not all labels will be used.

Answer 1

Given:

The expression is

$\sqrt{64}+\sqrt{-144}$

Rewriting it as a complex number in the standard form a+bi.

To find:

The missing values in the given simplification.

Solution:

We have,

$\sqrt{64}+\sqrt{-144}$

It can be written as

$\sqrt{64}+\sqrt{-144}=\sqrt{8^2}+\sqrt{-1\cdot 12^2}$

$\sqrt{64}+\sqrt{-144}=\sqrt{8^2}+\sqrt{-1}\cdot \sqrt{12^2}$

$\sqrt{64}+\sqrt{-144}=\sqrt{8^2}+i\cdot \sqrt{12^2}$   $[\because \sqrt{-1}=i]$

$\sqrt{64}+\sqrt{-144}=\sqrt{8^2}+i\cdot 12$

$\sqrt{64}+\sqrt{-144}=8+12i$

Therefore, the missing values are $-1,\ i,\ 12i$ respectively.