what is the most significant way of finding the cube root of a complex number?

what is the most significant way of finding the cube root of a complex number?

Struggling with this question.

have to find x and y values. Being i an imaginary number

Which of the following is a solution to the equation z3 = (1 + √3i) ? (A) 21/3[cos(23π/18) + i sin(23π/18)] (B) 21/3[cos(8π/9) + i sin(8π/9)] (C) 21/3[cos(17π/18) + i sin(17π/18)...

∑ ( 1/( (5i)^n + n) )

Let z1 and z2 be two complex numbers such that (z1-2z2)/(2-z1*conjug(z2)) is unimodular. If z2 is not unimodular, then find |z1|

part1. Let z=rcisθ where 0<θ<pi. show that Arg(z^2)=2θ. part2. sketch the region defined by {z: Arg(z^2)>pi/2} in the answers it shows region pi/4 to pi/2 and region 5pi/8...

If tan(Θ+i*Φ)=tanα+i*sec(α) Show that e2Φ=±cot(α/2) and 2Θ=(n+1/2)*Π+α

(a) If cos(Θ+i*Φ)=R(cosα+i*sinα),prove that e2Φ=sin(Θ-α)/sin(Θ+α) (b) if u=log(tan(Π/4+Θ/2)),prove that Θ=-i*log(tan( (Π/4) + (i*u)/2))

if cos(Θ+i*Φ)=cosα+i*sinα Prove that (i) sin^2(Θ)=±sinα (ii)cos(2Θ)+cosh(2Φ)=2

Sin(Θ+iΦ)=cosα+i*sinα prove that cos^4(Θ)=sin^2(α)=sinh^4(Φ)

if Sin(θ+Φ*i)=ρ(cosα+i*sin(α)) Prove that (i)(ρ)^2=1/2*(cosh(2Φ)-cos(2θ)) (ii)tan(α)=tanh(Φ)*cot(θ)

|Z-1| <= |Z-i| and |z-2-2i|<= 1. Sketch the region in the argand Diagram which contains the point P representing z. If P describes the boundary of this region, find the value of z. If P describes...

if tan(x+i*y)=A+i*B Show that A/B=sin(2*x)/sinh(2*y)

i want the invention of it.

Show that f(z)=[sin(PI/z)]/(z+2) is nowhere analytic for |z|<a , where a is a some positive number. Can you help me to solve this problem?

4√2(¡-1)

Write in standard notation, : a+bi 2(cos π/3+ isin π/3)

Evaluate Z ∫C(z^2 - z)/(2z + 1) dz where C is: (i) the unit circle in the counterclockwise direction; (ii) the circle |z − 2| = 1 in the counterclockwise direction. Do I use...

You are given four complex numbers in rectangular form: p=5+3j. q=2-4j. r=6j. s=-3-2j. Simplify the expressions below giving the answer in rectangular form: (i) p+s (ii)...

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