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1) Complex number z lies on the circle centered at 0 with radius 5. What is

$$|z^3|$$?

(The magnitude of z, denoted by $$\color[rgb]{0,0.36,0.11}|z|$$, equals the distance from the z to the origin on the complex plane.)

2) Riproarin' Ringo was roping a recalcitrant dogie. Ringo decided to give the dogie a reprieve by calculating $$|(1-i)^8|$$ before riding after the dogie. What answer should Ringo have found?

3) Suppose z  is a complex number such that z^3 = 100 + 75i. Find $$|z|$$.

4)The square of the non-real complex number z is equal to $$\overline{z}$$. What is the real part of z?

5)Find all complex numbers z such that $$|z - 3| = |z+i| = |z -3i|$$?

THANK YOU SO MUCH!!!!!!!!!!!

Oct 9, 2019

#1
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Thank you sooo much!!

Oct 11, 2019
#2
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Bruuh, I know you go to Aops and it is hard but this is not the way to succeed. What have you done to make your parents proud? PROBABLY NOTHING!!! At the end of the day, you are just someone who gets the answers right on the homework to impress your parents but you actually DON'T KNOW THE CONCEPT. Don't be the NORMAL ASIAN. Just press GIVE UP!! I hope my advice helped.

sincerely,

Your long lost Asian Brother from another mother

Oct 12, 2019
#3
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wait then y r u looking for the answers?

Oct 14, 2019
#4
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... but guest #2 is true try to give up.

Everyone wil think that you are better than you truly are, and when it comes to the real test! You will faIl!

Fail now or fail at the crucial moment, that is, press Give Up to learn how to solve the problem!

CalculatorUser  Oct 14, 2019