Consider z = 3StartRoot 3 EndRoot + 3i. What happens to the modulus and argument when z is raised to the 4th power?

Answer:

It's A

Step-by-step explanation:

Just took it and it matches

The modulus increased by 216 and the argument increased by π/2. Option A is correct

The number that constitutes of real and imaginary numbers are called complex numbers.

[tex]z = 3\sqrt{3} + 3i\\z^4 = (3\sqrt{3} + 3i)^4\\z^4 = 648(-1+\sqrt{3}i )[/tex]
Modulus and argument of  [tex]z^4[/tex] is given by.
[tex]|z^4| = 648\sqrt{1+3} \\|z^4| = 648\sqrt{4} \\|z^4| = 648*2\\|z^4| = 1296[/tex]
argument
[tex]\theta=tan^{-1}(\sqrt{3} /-1)\\\theta=tan^{-1}(-\sqrt{3} )\\\theta= -\pi /3[/tex]
similarly, the Modulus and argument of  z is given by.
Modulus
|z| = 6
argument
[tex]\theta=\pi /6[/tex]
Now comparing Modulos and argument of  [tex]z^4[/tex] and z
 [tex]z^4[/tex]/z = 1296/6 = 216
[tex]\theta=\pi /6+\pi /3\\\theta=\pi /2[/tex]

Thus, The modulus increased by 216 and the argument increased by π/2. Option A is correct.

Learn more about complex number here: https://brainly.com/question/28007020

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