Question

How do you find \[\left| 7i \right|\]?

Answer 1

Hint: From the question given, we have been asked to find \[\left| 7i \right|\].In simple terms the modulus of a complex number is its size. If you picture a complex number as a point on the complex plane, it is the distance of that point from the origin. If a complex number is expressed in the form of rectangular coordinates that is in the form of \[a+ib\], then it is the length of the hypotenuse of a right angled triangle whose other sides are \[a\] and \[b\]. Then, from Pythagoras theorem, we get \[\left| a+ib \right|=\sqrt{{{a}^{2}}+{{b}^{2}}}\]

Complete step-by-step answer:
From the question, we have been given that to find the modulus of \[\left| 7i \right|\].
If a complex number is expressed in the form of rectangular coordinates that is in the form of \[a+ib\], then it is the length of the hypotenuse of a right angled triangle whose other sides are \[a\] and \[b\]. Then, from Pythagoras theorem, we get \[\left| a+ib \right|=\sqrt{{{a}^{2}}+{{b}^{2}}}\]
We can clearly observe that from the given question that,
\[\begin{align}
  & a=0 \\
 & b=7 \\
\end{align}\]
Therefore, by using the above formula,
\[\Rightarrow \left| 7i \right|=\sqrt{{{7}^{2}}}\]
\[\Rightarrow \left| 7i \right|=7\]
Therefore, the absolute value of \[7i\] means the distance from the origin on the real axis is \[0\] and the distance on the imaginary axis is \[7\].
Hence the absolute value of \[7i\] is \[7\].

Note: We should be well aware of the concepts of modulus of a complex number. Also, we should be well aware of the usage of the modulus of a complex number. Also, we should be very careful while doing the calculation part. Also, we should be very careful while using the modulus of a complex number formula. We can also answer this question by substituting the value of $i$ as $\sqrt{-1}$ after that we will have $\left| 7i \right|=\left| 7\left( \sqrt{-1} \right) \right|=7$ .