5. Simplify to a C. Write answers in the form a + bi a, beR (g) (1+3i)(1 – 4i) (h) (5 – 2i)(-1+ i) (i) (-5 – 4i)(-5+ 4i)

Q: (b) Show that i10 is real, even though i or 10i is not.

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Q: .1 Determine the possible values of xif 2x|2|x-3|. Hence, give your answer in interval notation. 2…

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Q: Let z be the solution to z2 16 with - Im(z) > 0, and let w be the solution to w? 64 with Im(w) > 0.…

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Q: (1+i)·(10260°) (3–7i)+(9/120°) . Express your answer in rectangular form.

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Q: 6. Evaluate the following and leave your answer in standard form [(1 – 4i)-1 – 2(i + 1)-'[(3 – 4i)(i…

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Q: 4. (a) (i) Calculate (4 + 6i)².

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Q: 7. Evaluate jir de 1 2 + 2x2 Solution;

A: Topic:- definite integration  Note:- as per our guideline if more than one question uploaded than…

Q: 5. e-1+4i 5. cosh(2e3')

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Q: If z = 1+i then z5 is equal to: a. 4 + 4i b. 4 - 4i C. -4 - 4i d. -4 + 4i

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Q: 5. Simplify to a C. Write answers in the form a + bi a, beR (m) (6- 5i)2 4+i (n) 3 – 2i 5+ 3i (o)…

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Q: Solve the given differnetial eqation by undtermeind coefficients: y'' -4y = (x2 - 8)sin(2x)…

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Q: Show that x = 2 +3i is a solution to the equation x2 - 4x + 13 = 0.

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Q: Solve this question 2xy = (y)² + 1 Where y is absent

A: Given 2xy'y''=(y')2+1. We have to solve the given second order differential equation.

Q: 16. The roots of the equation x+ 2px + q = Odiffer by 1. Show that p q - 4.

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

Q: 18. Express the following in simplest form: (3+ 4i)?(3 – 4i)²

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Q: Let a = – 4i – 5j and b – 7i + 3j. Find a - b

A: we have  a→=-4i→-5j→ and b→=-7i→+3j→

Q: Which of the following is equivalent to the problem shown? In(2) where z = 10ei

A: To evaluate: lnz, where z=10eπi3. Let, z=x+iy. In polar form, z=reiθ+2nπi. Because, ez is parodic…

Q: Evaluate x - 2x +2 for x = 1 + i. x - 2x +2 evaluated for x =1+ i equals (Type your answer in the…

A: To evaluate x2-2x+2 for x=1+i

Q: If A=(1+i−1+2i3+2i2−i)A=1+i−1+2i3+2i2−ii and B=(i32−2i)B=i3i2−2i, findAB

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Q: nd a, b e R such that 4 5 a + bi 1- 2i i - 2 i- 2

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Q: Which of the following is equivalent to 3(5+ 2i)– 2(3– 6i)

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Q: | 2+4i -3 il %3D

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: The result of A(B x C)+ A × (B.C) may be: 10 2i+3j O 2i+2j-k

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Q: n Compute (2i? – 7i) = i=1

A: ∑i=1n2i2-7i

Q: What is the equivalent to the following expression in the form a + bi? (8+9i) – 3i[2i – (4- )]

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

A: In this question , the value of z is inserted into zw=-7-2i, and then it is solved for value of w.

Q: 4. Simplify 3- 2i / 1+i into the form a + bi 5. If 2 - a – 5i / (1 – bi) = 3 – 5i, find a and b

A: By Bartleby policy I have to solve only first one as these 2 are unrelated problems.These are…

Q: (24t³ – 30£-³) dt

A: ∫xndx=xn+1n+1+C

Q: Reduce Z= (1-2i) (3+2i), to the form a + ib а. 7+4i b. other С. 7-2i d. 7-4i O e. 4-4i

A: We will find out the required value.

Q: Suppose z-2z +x=5, What is the value of y ? | - 3 3 0 3i nim

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Q: 9. Find (2+31) A if A= [2-3i 5+8] -4 1-6-i 3-7i 5i

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

Q: - If A =3i and B=4i,then A B =... (where 0-1/2)

A: Given :A=3i    and B=4i

Q: I. Solve the following to Notation z = x + iy 1. In(-7) 2. z = i Z1 3. For Z, = 8+ 3i ; Z2 = 9 – 2i…

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Q: Solve the followings: 1- if zl=2+3i, z2=-1+i and 23=3-2i, give an expression for zlz2 + (23).

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Q: Solve the following iñitial + 6y = 2t %3D with y(1) = 2.

A: We need to solve the differential equation tdydt+6y=2t ; y(1)=2

Q: Let A = |'5 [1-7i 1+4i Find A 31 - 7i 5 l1+ 4i 3il + 7i li – 4i -3il 5 (b) (0) [' ;" + 7i 1-4i - 7i…

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Q: 2. i 3-2i 5

A: We have to compute the indicated power -i3-2i5

Q: 11. If AB = 8z + 5, CB = 10z – 1, and BD 1 AC, solve for z.

A: Given, AB=8x+5, CB=10x-1

Q: 5. Simplify to a C. Write answers in the form a + bi a, be R -8+ 3i (p) -9 – 5i V5 + 2i (q) 1- 2i 17…

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Q: Solve the following problem 3 z +8i=0

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Q: answers in terms of i,j and k.

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Q: 9) Simplify, then write your result in standard form: (6 + /-9) – 2i + 10 – J16. (a) 16 - 3i (b) 13…

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Q: Solve the following expression in the form of a+ bi : i) (-3+4i)(7–1li) 11-2i -2-5i 2+3i 1 +. 2-3i…

A: Since you have posted multiple subparts, as per our policy we will answer first three subparts.…

Q: Solve: Subject to 2wt+3ux + 4u = 0 u (x,0) = x² in R. x [0,00)

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Q: .neN' E (4i+1) = 2n² +3n+1 ||

A: We have to proof

Q: (b) Show that ii is real, even though i or 5i is not.

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Q: If a = 3i +j-k, b = 2i -j+k and c= 5i + 3k , find (2 a +b).c.

A: Given a→=3i+j-k, b→=2i-j+k, c→=5i+3k 2a→+b→=2(3i+j-k)+(2i-j+k)          =6i+2j-2k+2i-j+k…

Q: Consider the following definitions of imaginary numbers: x=4−2i y=6+7i z=5i Then, x+y−2z=?

A: We plug the given values in the expression x+y-2z

Q: If r(t) = Give exact answers in component form. a) 7(0) = 57

A: