Question

How do you simplify $i(2 + i)$ ?

Answer 1

Hint : To solve this question, the brackets simply need to be opened, and the multiplication operations need to be performed. The answer will be obtained once you simplify the expression that was generated after multiplying the complex numbers. For this, remembering the basic identities of iota will be helpful.

Complete step-by-step answer :
We have to simplify this expression: $i(2 + i)$
We need to open the brackets of this expression to simplify it into a complex number.
Now, we know that the square of $i$ is $- 1$ , since $i$ is equal to the imaginary value of the square root of . $- 1$ . .
We will use this fact for the simplification of this expression.
On opening the brackets, we will obtain the following:
$i(2 + i) = 2i + {i^2} = 2i - 1$
Thus, the simplified expression for $i(2 + i)$ comes out to be $2i - 1$ .
So, the correct answer is “ $2i - 1$ ”.

Note : A complex number is a number that has both real and imaginary parts. Technically every number can be considered as a complex number, because all numbers have both of the two parts of a complex number. It’s just that the value of the missing part can be assumed to be zero. To multiply complex numbers, all parts of a complex number get multiplied by all parts of the other complex number. The result is then simplified to yield the final answer.