217 Answered Questions for the topic Complex Numbers

Complex Numbers

06/26/18

Find the modulus and argument of: z= ((1 +j2)^2 * (4−j3)^3) / ((3 +j4)^4 * (2−j)^3)
Ans: (√5)/25,−2.035 Please show step by step
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Complex Numbers

06/22/18

Given z1=e^(iπ/4) and z2=e^(−iπ/3) , find the arguments of (z1^3/z2).
The answer in the book is −11π/12. Please show step by step.
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Complex Numbers

06/22/18

Find the real and imaginary parts of z when: 1/z = (2/(2+3i)) + (1/(3-2i))
The answer on the book is 7/5 + i 4/5. However, I couldn't solve it.Please show step by step.
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Complex Numbers

05/31/18

radical sums
whats the sum of the square root of -2 and the square root of -18
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Complex Numbers Calculus Precalculus

05/14/18

Write the complex number in polar form. Express the argument in radians. -5+5squareroot3 i
Show all work  
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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
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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... more
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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?)
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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?
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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.  
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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
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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)... more
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Complex Numbers Math Help Sum Problem

02/11/18

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) )
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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|
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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... more
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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
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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))
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Complex Numbers Functions Complex Conjugate

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
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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)
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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)
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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... more
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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)
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Complex Numbers

01/03/18

who introduced the complex number?
i want the invention of it.
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Complex Numbers Calculus Complex Calculus 3

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?
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Complex Numbers

12/02/17

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