212 Answered Questions for the topic Complex Numbers

Complex Numbers

05/07/18

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

(1+w)7 = A+Bw

05/04/18

#### 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...
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Complex Numbers Taylor Series

04/24/18

#### 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

04/16/18

#### 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

03/22/18

#### 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

03/08/18

#### -2x+3yi-5-2i=x-8i+x-4i

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

Complex Numbers

03/08/18

#### 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)...
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#### How do I find convergence of this sum, without using integral test ( i is imaginary unit; sum goes from 1 to inf ) :

∑ ( 1/( (5i)^n + n) )

Complex Numbers Algebra

02/11/18

#### COMPLEX NUMBERS QUESTION

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|

01/22/18

#### 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...
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Complex Numbers Functions

01/16/18

#### 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

01/16/18

#### 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))

01/15/18

#### 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

01/15/18

#### Functions of Complex variables

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

Complex Numbers Functions

01/15/18

#### 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

01/14/18

#### 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...
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Complex Numbers Functions

01/13/18

#### Functions of Complex Variable

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

12/23/17

#### 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 Graphing

11/29/17

#### Write in standard notation:

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

Complex Numbers

11/13/17

#### 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)...
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#### 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

10/11/17

#### What is (ab) the whole conjugate

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

10/08/17

#### 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

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