4. Let z = -4 + 3i and zw = -7 – 2i. By showing clear steps, find w in the form of a+bi.

Q: Suppose z = x + 2i and u= 3+ yi where x, y E R. Find the smallest positive value of x z + u for…

A: Substituting z=x+2i and u=3+yi in z+uz-u:  z+uz-u=x+2i+3+yix+2i-3+yi           =x+3+2+yix-3+2-yi

Q: Let 7(t) = Find dt (don't include the +C)

A:

Q: Given z = -5+ 3i and z2 = 3 – 6i, express in the form a + bi %3D i. 4z1* – Z2 ii. Z2

A: Complex Cartesian form

Q: Given that the characteristic equation has the following roots , what is the complementary solution?…

A: Given are the roots of a characteristic equation    1±3i,1±3i⏟,  2,2,2,2,4⏟       Repeated…

Q: 17. Given a = 4 – 4i and az = 4 + 3i, express %3D :11 in the form a + bi. a, az CLONE Dec 19

A:

Q: If Z= 3 – 2i and W = 4 – I, write  ZW in the form a + bi

A: Z=3-2i  &  W=4-i

Q: 8. Solve the following IBVP: U = u + sin(3nr), 00, u(0, t) = u(1, t) = 0, t20, u(r,0) = sin(72),…

A: Given ut=uxx+sin(3πx), 0<x<1, t>0u(0,t)=u(1,t)=0, t≥0,u(x,0)=sin(πx), 0≤x≤1

Q: Show that the following gn are harmonic and find its conjugate u=3x^2y+2x^2_y^3_2y^2

A:

Q: Exercise 3: Solve the following equation for x and y where 3 xy – 2i + x + 2xyi – 5 = -- 3i 2

A: Solution of the equation

Q: Say that E = Ãek™, where the components of A and k are real and constant, i.e. they aren't imaginary…

A: A vector is a quantity that has both magnitude and direction. In general, vectors are represented as…

Q: ) Compute the four 4th roots of −T + Ti where T=7

A:

Q: Suppose ū = 2j + k, ū = 2i – 4j + 2k and w = -5i – j+ k. %3D Compute the following values:

A:

Q: What is the image of ALMJ by Ro90? Ro,90? a. AJKL b. AKLM c. ALMJ d. ДМJK

A: Here we have to find the image of the ∆LMJ by Ro,90

Q: Given z = 3– 4i and w = -1- 2i, compute the following and express your final answers in the fe-n a +…

A:

Q: Let w e H and suppose that (1+ i)w(1+ 2j) = 1+ k. nd w (your answer should be in the form a + bi +…

A: Given function is, 1+iω1+2j=1+k

Q: 4. Find the distinct roots of z for the following equation, z4 = 3i. %3D 5. Prove by taking z = a +…

A: Q4) Given that z4=3i So z4=3iz4=3cosπ2+isinπ2z4=3cos2nπ+π2+isin2nπ+π2         Since sin and cos are…

Q: Reduce to the form a + bi: a. sin (2 – i); b. cosh (1+ i).

A: Given: sin2-i cosh1+i To do: Reduce the given into the form a+bi.

Q: HW/ IF 2, = 1-3i, Zz=-2+si & Z3 = -3-4i determine as a+bi ,0 .0 z,-2.. 2;

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: Find the imaginary component of In(z + w) if z = 16 + 6i and w=7+8i . Round off your final answer in…

A: Complex number, imaginary part

Q: ez = -2

A:

Q: Reduce to the form a + bi: a. sin (2 – i); b. cosh (1 + i).

A: Solution:-

Q: Suppose z = a+ bi, w = u + iv, and

A:

Q: Find the imaginary component of In(2z + w) if z = 11 + 9i and w=10+4i .

A:

Q: Given that the characteristic equation has the following roots, what is the complementary solution?…

A: We will find out the required complementary function.

Q: 18 In(z – 3) Question 10) Find I = -dz, where C = Iz - 2 + 4i| = 4, Ccw z2 + (4 + 4i)z + 3+ 4i

A:

Q: given z=1-8i and w=3+5i, find the following. a.   zw b.   conjugate of w. c.   z+w

A: Complex number

Q: Use the substitution x = et, to solve the following Cauchy-Euler equation: x²y// – 4xy/ + 4y = x³ In…

A: We will find out the required solution for given Cauchy Euler differential equation.

Q: Show that the following equations have at least one solution in the give x cos x – 2x + 3x – 1 = 0,…

A: Given: To explain the given statement as follows, Here, the equation is  .

Q: Let z = 1- V3i and w = - v2 + vZi . Evaluate а. w 2 ( cos 12 i sin 12 O b. w -= 2 (COS 117) +i sin…

A: Given z=1-3iw=-2+2i

Q: | 3t In(t)dt

A: We have to solve this question with the help of by parts integration. ∫fgdx=f∫gdx-∫∂f∂x∫gdxdx It is…

Q: Let z = 8+ 8i and w = 5 – 3i . Find out the following in the x + ijorm. 1. z2 + w 2. žw? 1 3. wz 4.…

A: Given that  Z=8+8i and w=5-3i

Q: Suppose NOL -> QRM is a reflection across the x-axis. If O(9, 4) what is the y coordinate of R?

A:

Q: Show that the following gu are harmonic and find its conjugate U = 3x²³y + 2x² - y²³-2y²

A:

Q: if क f z₁ = 2 ( 65 30 +isin 30) and Z₁ = (Cos60 +isin60), Find the following Z₁ * Z₁ له الله چه

A: Here we have z1=2cos30°+isin30° and z2=13cos60°+isin60° We have to find 1) z1·z2 and 2) z2z1

Q: Exercise 3: Solve the following equation for x and y where 3 xy – 2i + x + 2xyi – 5 =- 3i | 2

A: This kind of problem we can solve by comparing the real and imaginary parts and after that solve the…

Q: Find each of the following in rectangular (a + bi) form if z = 2 – 3i; if z = x + iy. 1+z 23. 1- z

A: z = 2 -3i  given , To solve 1+z1-z, =1+2-3i1-2-3i = 3-3i-1+3i = 3-3i-1+3i×-1-3i-1-3i,…

Q: Use DeMoivre's Theorem to find the following. Write your answer in standard form. V2 cis- 20 O…

A: Given (√2cos(9π/20))5

Q: Given that the characteristic equation has the following roots , what is the complementary solution?…

A:

Q: 2.18 Obtain the canonical form for the following elliptic PDES: a?u a?u (a) ax? дх ду ay? a?u a?u du…

A:

Q: 1. Express in the forrm a + bi. a) (1+ 3i)(1 – i) b) (-3+ i)/(7 – 3i)

A:

Q: 5. Use the Chain Rule to find dw dt where w = sin 12x cos 4y, x=7, and y =t". :- dw (Type an…

A:

Q: Let z, = 4 – 2i ; z2 = 3 + i ; z3 = 1 + 2i || -

A: Given z2 = 3+i and z3 = 1+2i

Q: a. Let z1 = 2 – 3i, z2 = 3 + 4i and z3 = 1– V3i. Find z1z2 + z3 then sketch it on Argand diagram.

A: Simplify Z1Z2 + Z3 in simplest form and convert it into polar co-ordinates.

Q: If z=2e(i pi/20), use De Moivre's theorem to compute z5

A: Use demoivre theorem

Q: Find the four fourth roots of z = 256(cos4pi/3 + i sin4pi/3)    w0= w1= w2= w3=

A: Solution...

Q: If the coordinates of any two points ₁ and ₂ are (x₁, y₁) and (x2, ₂), respectively, then prove that…

A:

Q: S(1,9) =2Inc* + y° )• 3y° tan"), then prove that B.(i) If дхду дудх

A:

Q: 2. find the the following equation in simplest arbi Saution set of form. X-3x + 9 = 5Y-10

A:

Q: Suppose NOL -> QRM is a reflection across the x-axis. If O(1, 9) what is the y coordinate of R?

A:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.