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)...

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)...

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

(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))

∑ ( 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|

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

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(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?

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)

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

For some reason 1+i = root 2 * e ^ pi / 4 which i dont understand how so I would like an explanation for this...

Find the nth roots of the complex number for the specified value of n: -17i, n=6

4√2(¡-1)

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

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)...

A. Calculate the perimeter of the polygon whose vertices are the complex fourth roots of 1. B. Calculate the perimeter of the polygon whose vertices are the complex ninth roots of 1....