Question

If z=7+24i find the amplitude

Answer 1

Therefore Amplitude of $z=7+24i$  is  $25$

Step-by-step explanation:

Given;

$z=7+24i$

To find the Amplitude of a complex number let us assume that, a complex number $z=x+yi$ where $x> 0$ and $y> 0$ are real,$i=\sqrt{-1}$ and $x^{2} +y^{2} \neq 0$

Then,

Amplitude of $z=\sqrt{x^{2} +y^{2} }$

From given question,

Where $x=7$ and $y=24$

$\left |z \right |=\sqrt{7^{2}+24^{2} }$

$\left |z \right |=\sqrt{49+576}$

$\left |z\right |=\sqrt{625}$

$\left |z\right |=25$

Therefore Amplitude of $z=7+24i$  is  $25$