Question

How do you find $\left| 7i \right|$?

Answer 1

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,

& a=0 \\\ & b=7 \\\ \end{aligned}$$ Therefore, by using the above formula, $$\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 $\left| 7i \right|=\left| 7\left( \sqrt{-1} \right) \right|=7$ .