Question

If Z = 12 + 5i, then |Z|^2

Answer 1

Answer:

$\sf \: z = 12 + 5i$

$\sf \: {z}^{2} = {(12 + 5i)}^{2}$

$\sf{z}^{2} = {12}^{2} + 2(12 \times 5i) + {5i}^{2}$

$\sf{z}^{2} = 144 + 2(60i) + 25 {i}^{2}$

$\purple{ \sf \: {z}^{2} = 144 + 120i + 25 {i}^{2} }$

Answer 2

Answer:

If $Z=12+5i$  then $|z|^2=169$

Step-by-step explanation:

Given :

We are given a complex number $Z = 12+5i$

To Find :

The value of  $|z|^2$

Solution :

Since we are given the complex number  $z = 12+5i$

We have to find the value of  $|z|^2$

$|z| = \sqrt{12^2+5^2}$

   $= \sqrt{144+25}$

   $= \sqrt{169}$

   $= 13$

Hence we have calculated the value of |z| = 13

Now we have to calculate the value of $|z|^2$

$|z|^2 = 13^2 = 169$

Hence the value of $|z|^2=169$

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