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

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)...

please help I have no idea what this means and I need the work to show how to do it

Here no plus or minus is there, then how could we able to find conjugate?

Consider complex numbers Za=1+i and Zb=u+vi where u<0<v. If S represents the area bounded by the origin, Za and Zb, find Arg(Zb) for which real(Zb) + Imag(Zb) = (2/root3)S

How do you put the complex number -2+i into a form of e^{ix} ? with i = sqrt(-1) x= angle...

Find the fifth roots of the complex number: cos(5pi/4)+isin(5pi/4)

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

Find the nth roots of the complex number for the specified value of n. 2-2i, n=4

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