212 Answered Questions for the topic Complex Numbers

Complex Numbers


Find the value of A and B......if w is the complex cube root of unity

(1+w)7 = A+Bw


i need to solve a word problem....

Nba basketball legend Michael Jordan had a 48in. vertical leap. suppose that Michael jumped from ground level with an initial velocity of 16ft/sec. Michaels height h (in feet) at a time t seconds... more
Complex Numbers Taylor Series


What is Taylor series of ln(z-3)(z-1)?

Around 0? And what is the radius of convergence? (And the domain of the function?)
Complex Numbers


how can i find the cube root of 88+16i (unable to solve by DE MOIVRE'S theorem )??

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


i need to find the real numbers of x and y which satisfy the equation : 2 + x - yi / 3x + yi = 1 + 2i

Struggling with this question.  
Complex Numbers Equations, X And Y



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


Which of the following is a solution to the equation z3 = (1 + √3i) 

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) (D)... more
Complex Numbers Algebra



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|


Need help with complex numbers and locus

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 to 3pi/2... more
Complex Numbers Functions


Functions of a Complex variable

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


Functions of Complex Variable

(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))
Complex Numbers Functions Complex Conjugate


Functions of a complex variable

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


Functions of Complex variables

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


Complex numbers

ifSin(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)
Complex Numbers


Complex Numbers

|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... more
Complex Numbers Functions


Functions of Complex Variable

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


who introduced the complex number?

i want the invention of it.
Complex Numbers Calculus Complex Calculus 3


Complex Analysis - Analytic Functions

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?
Complex Numbers


find all the cube roots of 4surd 2(i-1)

Complex Numbers Graphing


Write in standard notation:

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


complex numbers in rectangular form

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) p+q(iii) r s (iv) r(p-q)(v)... more
Complex Numbers Sum Conjugate


the conjugate of a sum is the sum of the conjugates of the individual complex numbers

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


What is (ab) the whole conjugate

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

Complex number to exponential form

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

Still looking for help? Get the right answer, fast.

Ask a question for free

Get a free answer to a quick problem.
Most questions answered within 4 hours.


Find an Online Tutor Now

Choose an expert and meet online. No packages or subscriptions, pay only for the time you need.