An Imaginary Common Sense Problem

Algebra Level 3

The number of conduct cuts I have in math for "not following directions" and "not bringing materials to class" is m m ,where m m is n + 1 {n}+{1} ,where n = a + b {\sqrt{n}}={a}+{b} ,where a + b i = ( 1 ) 3 / 4 {a}+{b}{i}=({-1})^{3/4} . Note that I mean the greatest possible value of a+b. Oh right.FIND M


The answer is 3.

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1 solution

Aaryan Vaishya
Sep 29, 2019

1 3 / 4 = i {-1}^{3/4}={\sqrt{i}} .We can know that sqrt(i)=a+bi,so squaring both sides we have a^2-b^2+2abi=i.We can match coefficients to get a=b and 2a^2 =1.So both a and b are +/- 1/sqrt2. 1/sqrt2+1/sqrt2=2/sqrt2 =sqrt2.So n = 2 and m=3.

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