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f(z)=z²-(6+-4i) z+(-27+12) has 2 roots: z₁ and z2, sorted in an increasing manner according to the modulus and the the argument (between 0 and 2π2π: (|z1|<|z2|) or (|21|=|z2| and arg(z₁)

f(z)=z²-(6+-4i) z+(-27+12) has 2 roots: z₁ and z2, sorted in an increasing manner according to the modulus and the the argument (between 0 and 2π2π: (|z1|<|z2|) or (|21|=|z2| and arg(z₁)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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f(z)=z<-(6+-4i) z+(-27+12) has 2 roots: z1 and z2, sorted in an increasing manner according to the modulus and the the argument (between 0 and 2T2n: (|z1|</z2l) or (|z1l=lz2| and arg(z1)<arg(z2)) or (z1=z2) 1.Calculate Re(z1/z2) 2.Calculate: arg(z1+z2^(1/3)) (root with minimal positive argument) 3.Calculate |z1l 4.Calculate arg(z1/z2) (in radians between 0 and 2t)
Transcribed Image Text:f(z)=z<-(6+-4i) z+(-27+12) has 2 roots: z1 and z2, sorted in an increasing manner according to the modulus and the the argument (between 0 and 2T2n: (|z1|</z2l) or (|z1l=lz2| and arg(z1)<arg(z2)) or (z1=z2) 1.Calculate Re(z1/z2) 2.Calculate: arg(z1+z2^(1/3)) (root with minimal positive argument) 3.Calculate |z1l 4.Calculate arg(z1/z2) (in radians between 0 and 2t)
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