1. Let z = 2 – 3i and w = -3+ 2i. (a) Find z + w and z – w. (b) Find zw and (c) Find zu and žw. (d) Find (z – w)? + 2zw.

Q: (a) cos(iz) = cos(iz) (b) sin(iz) = sin (iz) for all z; if and only if z = nлi (n = 0, +1, +2, ...).

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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: (а) 8а + 2у + 32 %3D 0 (b) z = sin(x) + cos(y) (1) (c) z = sin 2+x2+y? (d) z = ey II 2. 10 2 0- -5…

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Q: 8 +10x-32+x? cos 2x 4 Find : (a) y = %3D x2

A: Given y we have to find dy/dx as shown below

Q: Show that the equation 2²2 2 2²y Əy +2k c². əx² de ² Ət possesses solutions of the form 0 - kt Σ Cre…

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Q: Find L[et tsin(2t) - e-2t+3 +e-2t cos 3t]

A: BY USING THE LAPLACE TRANSFORMATION RULES  WE GET OPTION (D) IS CORRECT OPTION.

Q: (b) (cos(x) (2x + 3))'

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Q: 8. If fx) = cos (2x), findf '(). TC %3D a. b. c. 1 d. -1

A: The given function is f(x) = cos2(2x) Differentiate with respect to x using chain rule…

Q: 5. Find the general solutions of the equations i) Zx - 4z,, – 5z, +10z, = cos(x+3y)-sin(x+3y) %3D

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

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: de cos² 0

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Q: iv) z, = ei01 ,Z2 = el62 then z,. z, = ei(81-02)

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Q: Find Duf at P. 3 4 f (x, y) = sin(3x – 4y); P(4,3); u = i j %3D - - NOTE: Enter the exact answer.…

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Q: If z = +i then Im(coshz) A) –sin1sinh4 B) cos1cosh4 e* +e* C) cos1 2 D) sin1cosh4 E) sin1

A: Topic:- hyperbolic function and complex number

Q: If x, y and z are independent variables and f(x, y, z) = x sin(y + 3z) of then find ôz .

A: Here, x,y,z are independent variables. Given function is f(x,y,z)=xsin(y+3z)

Q: (D* — 81)у %3D0 A. y = c1e3* + c2xe³* + c3e¬3x + C4xe¬3x B. y = ce3* + Cze-3* + C3 cos 3x + C4 sin…

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Q: T (4) = %3D .a 12.b 0 6.cO 24 dO

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Q: 4.1 z + cos(72) -dz, c z(z² +1) with C : |z – i| =.

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

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Q: 1. a. Let In = exp (nx) sin (exp (x)) dx. By making an appropriate substitution, or otherwise,…

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Q: Find all values of the complex function of z for the e^(3z)=1z=x+iy

A: Its given that e3z = 1.  Given, z=x+iyWe need to sovle for z.

Q: What is the exact value of cos ZPQR? 3. R. 21 16 7 16 3 16 4. 1/4

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Q: Q1:-/ Verify by direct substitution that y, = epx cos qx and y2 = ePx sin qx , are solutions of the…

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Q: Solve J²u = Ət² u (0, t) = u (x, 0) = J²u 4- 2 მ2 u (π, t) = 0 sin (2x), 0 0 (x, 0) = 0 Ju Ət

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Q: 2) f(3x + cos(x))[3x +2sin(x)-31dx = A) 3x+2sin(x)- 3+C B)13x+ 2sin(x)- 31 +C C) other

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Q: c) If f(x, y)= e" cos 2x, then show that = 0.

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Q: If f(x) = cos (x) + 3x + 2, x e [0, 1], then f-(5) 3= %3D A) cos + 17. B) 5m cos +17 C) 0. D) 2. E)…

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Q: 1 a) r(t) = ( In(7t), Vi + 4, V17 - t b) r(t) = ( Vi – 3, sin(81), ² ) t 3t 1/3 c) r(t) = /2 – 64 -

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Q: What is the value of csc ( 1) 137 7T + cos( V3+2/2 O -V3-2/2 -V3+2/2 2 V3-2/2

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Q: 5(t - )cos3t) 3 252 + 18

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Q: A) u-substitution with u = 7x³ +5 B) u-substitution with u = 3x² u-substitution with u = 3x² dx…

A: Integration

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: When the general solution of y" + 4y = tan2x is written as y = U(x)cos2x + V(x)sin2x then which of…

A: The given differential equation is y''+4y=tan2x. The auxiliary equation of the corresponding…

Q: Determine c, and c2 so that y(x) = c, sin 2x + c2 cos 2x + 1 will satisfy the conditions y () = 0…

A: Consider the function: yx=c1sin 2x+c2cos 2x+1. Calculate c1 and c2. Given yπ8=0 and y'π8=2.   Since…

Q: If f(x) = cos (-x) + 3x + 2, xE [0,1], then f"(5) = %3D A) cos + 17. B) cos()+17" (Sm C) 0. D) 2. E)…

A: Solution of question as follows

Q: (b) Determine whether u(x,t)= e' sinx is a solution to L

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Q: A. Find y' if 1. y = x² cos² 3x

A: y=x2cos23xApply product rule to differentiate the given function y with respect to…

Q: 7 Jlgull sin(2) = e-e- 2i eiz-e-iz 2 et +e-iz 2i e -e-i: 2i

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Q: Find T, N, B, K and t for r(t) = (3csc^3t • sin^6t) i + (3sec^3 t • cos^6t)j + 5k

A: given that                                             r→(t)=3csc3tsin6ti^+3sec3tcos6tj^+5k^ now…

Q: What is r = -12 2 cos 0-7 sin e 2y - 7x = -12 in Cartesian form? x² + y² = -12 2x-7y

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Q: r(cos0+isin 0) with 0 (exact) in (0°,360°): а. z = 12-12i Z, =-3-3i z, =-4V3+ 4i b. с. Z3 = %3D

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Q: (5e" + 6x + 5 cos z)da

A: The solution is given below

Q: Determine c1 and c2 so that y(x) = c1 sin 2x + c2 cos 2x + 1 will satisfy the conditions y(pi/8) = 0…

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Q: lim,-9+76i (z² + 18z) = x + iy,

A: The solution is given as

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

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

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Q: The auxiliary roots of the auxiliary equation associated with a certain HLDE are m=±3, ±3i, ± 3i.…

A: Solution is given as below:

Q: Show that, for any constants k' and 'a', u = sin(kx) sin(akt) is a solution of the equation Ut =…

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Q: Solve the diffesential equation 2ber 十X

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