Question

Fix a ∈ C and b ∈ R. Show (prove) that the equation |z^2|+Re(az)+b = 0...

Fix a ∈ C and b ∈ R. Show (prove) that the equation |z^2|+Re(az)+b = 0 has a solution if and only if |a2| ≥ 4b. When solutions exist show the solution set is a circle.

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Fix a ∈ C and b ∈ R. Show that the equation |z2|+Re(az)+b = 0 has...
Fix a ∈ C and b ∈ R. Show that the equation |z2|+Re(az)+b = 0 has a solution if and only if |a2| ≥ 4b. When solutions exist show the solution set is a circle. (proof in the form of a generic If and only if proof).
Find the set of complex numbers z satisfying the two conditions: Re((z+1)^2)=0 and Im((z−1)^2)=2. Here Re(a...
Find the set of complex numbers z satisfying the two conditions: Re((z+1)^2)=0 and Im((z−1)^2)=2. Here Re(a + bi) = a and Im(a + bi) = b if both a, b ∈ R. Then find the cardinality of the set.
(a) Let a,b,c be elements of a field F. Prove that if a not= 0, then...
(a) Let a,b,c be elements of a field F. Prove that if a not= 0, then the equation ax+b=c has a unique solution. (b) If R is a commutative ring and x1,x2,...,xn are independent variables over R, prove that R[x σ(1),x σ (2),...,x σ (n)] is isomorphic to R[x1,x2,...,xn] for any permutation σ of the set {1,2,...,n}
Find the value of z which fulfill the equations below az^2+bz+c=0         a must not be 0...
Find the value of z which fulfill the equations below az^2+bz+c=0         a must not be 0 z^3 = -1 z^4 = -i16 z^4 = -1+i These are from complex number roots section
Prove that the set S = {(x, y, z) ∈ R 3 : x + y...
Prove that the set S = {(x, y, z) ∈ R 3 : x + y + z = b}. is a subspace of R 3 if and only if b = 0.
a) Let f : [a, b] −→ R and g : [a, b] −→ R be...
a) Let f : [a, b] −→ R and g : [a, b] −→ R be differentiable. Then f and g differ by a constant if and only if f ' (x) = g ' (x) for all x ∈ [a, b]. b) For c > 0, prove that the following equation does not have two solutions. x3− 3x + c = 0, 0 < x < 1 c) Let f : [a, b] → R be a differentiable function...
1.49 Two particular solutions of the equation 4f''(z)+f(z)=4f'(z) are f1(z)=ez/2 and f2(z)=zez/2. a) Show that any...
1.49 Two particular solutions of the equation 4f''(z)+f(z)=4f'(z) are f1(z)=ez/2 and f2(z)=zez/2. a) Show that any linear combination Af1(z) + Bf2(z) is also a valid solution to the differential equation. b) Find the particular solution that satisfies the conditions f(2)=14e and f'(2)=12e.
13. Let R be a relation on Z × Z be defined as (a, b) R...
13. Let R be a relation on Z × Z be defined as (a, b) R (c, d) if and only if a + d = b + c. a. Prove that R is an equivalence relation on Z × Z. b. Determine [(2, 3)].
Define a binary operation on R 2 − {(0, 0)} by (a, b) · (c, d)...
Define a binary operation on R 2 − {(0, 0)} by (a, b) · (c, d) = (ac − bd, ad + bc). Prove that (R 2 − {0}, ·) is an abelian group. (You do not need to prove that the operation is closed.)
let A (1 , 2, -3), B (2, 1, 4) and C (0, 0, 2) be...
let A (1 , 2, -3), B (2, 1, 4) and C (0, 0, 2) be three points in R^3 a) give the parametric equation of the line orthogonal to the plane containing A, B and C and passing through point A. b) find the area of the triangle ABC linear-algebra question show clear steps and detailed solutions solve in 30 minutes for thumbs up rating :)
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT