Question

How do you simplify $|20+21i|$?

Answer 1

We are given an expression which we have to simplify. It is a question based on complex numbers. And the expression is to be simplified, so we will use the formula which is as follows, $|a+ib|=\sqrt{{{a}^{2}}+{{b}^{2}}}$. We will substitute the given expression in the formula mentioned. Solving which will give us the simplified form of the expression given.

Complete step by step solution:
According to the given question, we are given an expression which we have to simplify as much as possible. We can see that the given question is based on a complex number.
To simplify the given expression, we will use the formula, $|a+ib|=\sqrt{{{a}^{2}}+{{b}^{2}}}$. So, in order to simplify the given expression, we will simply substitute the values from the given expression into the above mentioned formula.
The given expression we have is,
$|20+21i|$-----(1)
Using the formula, we know, we have,
$\Rightarrow \sqrt{{{20}^{2}}+{{21}^{2}}}$----(2)
So, we have the root of the sum of ${{20}^{2}}$ and ${{21}^{2}}$.
We know that, ${{20}^{2}}=400$ and ${{21}^{2}}=441$, so substituting these values in the equation (2), we get,
$\Rightarrow \sqrt{400+441}$----(3)
Now adding up the terms, we get,
$\Rightarrow \sqrt{841}$----(4)
We know that square of 29 is 841, so we have,
$\Rightarrow 29$
Therefore, the simplified form of the given expression is 29.

Note: The expression should be written correctly and while substituting the values in the formula $|a+ib|=\sqrt{{{a}^{2}}+{{b}^{2}}}$, the values should be correctly substituted and carefully evaluated. Also, the square of the numbers up to 30 should be known.