72 Engineering Mathematics (1) (3200-0202) Lecture No.2 Ass. Prof. Mohamed M. Fathy -AIBaha University, KSA In Problems 21-24, write each complex number in polar form. V 21. (3 – 3i)(5 + 5v3i) 22. (4+ 4i)(-1– i)-

Q: (4.4) (a) Find the roots of z – 1 (b) Find in standard forms, the cube roots of 8 – 8i (c) Let w = 1…

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: Evaluate every complex number equations given. 1) z = e(4+j3) In(6230°) 10 2) z = (-¡)(- 3) z =…

A: Given:  1. z=e4+j3ln6∠30° 2. z=-j22-j2210 3. z=45+j3 Evaluate each of the given complex numbers. "As…

Q: Question two. (3+3) Find the set of all complex numbers satisfying the equations. (1) (z + 1)3 = (z…

A: 1 z+13=z+23 z3+13+3×2×1z+1=z3+23+3×2×2z+21+3z2+3z=8+6z2+12z⇒6z2-3z2+12z-3z+8-1=0⇒3z2+9z+7=0…

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

A:

Q: (d) Re(cosh z) = cosh x cos y, Im(cosh z) = sinh a sin y. (e) | sin z|? = sin² x + sinh? y, (f) |…

A:

Q: Given the following three complex number: Z1=2+ j6, Z2 = 6– j3, and V = 30+ j40 V If I =V (Zl+Z2)…

A: When two complex numbers are added, then the real parts are added together and the complex parts are…

Q: 1. Solve the following complex number problems: a. Simplify: i55 + 3i35 + 2i23 – 2i1² (5+31)(3–41)…

A:

Q: 4. Parts (a) and (b) below refer to the numbers z = 1+ 3i and w = -3+ 2i. You must show the work…

A: For the solution of the problem follow the next steps.

Q: In Problems 22-25, write each expression in the standard form a + bi. 14 22. [3(cos 20° + i sin 20°)…

A: We have, 3cos20°+isin20°3 As we know that, from the De Moivre's theorem cosθ+isinθn=cosnθ+isinnθ

Q: Find the Modulus of the following complex numbers: (a) 3 (b) (i + 1)(2 – i) (c) 2 – 3i

A:

Q: In Problems 2 and complex numbers in surd form. 2. (a) 2+13 (b) 3. (a) -j3

A:

Q: roblems 1. 2

A:

Q: 21-5 1. a) Convert the complex number to the form a + bi. 1-3i 1. b) P(x) = x* – 3x' +5x² - 2 What…

A:

Q: 2. Write each of the functions in the form Aet cos Bt +iBed sin Bt, where a, B, A, and B are real…

A: To write each of the given function in the form  A* eatcos(bt)+Beat sin(bt) . We apply three…

Q: a) Express the complex number (5-2i) in the form a +bż b) Epress the complex number be low in the…

A: Rational Numbers: All the numbers which can be written in the form of pq. Here, p and q are integers…

Q: Question No. 3, Part (A) i. From the Euler Relatins, deduce that e-3i"/4 = -(1+ i) ii. Find the…

A:

Q: a) Simplify the following expressions in standard form. (i) (5i"+6i° +2i?–3i*)+(-4+7i) 7-4i (ii) 2–…

A:

Q: 6. Given the triangle in the figure below, use complex numbers to rotate it 7/3 radians clockwise…

A: First we will find the coordinates of a given triangle in complex form.Then we will write the…

Q: |74. Notice that (r cis 0)² = (r cis 0)(r cis 0) = ² cis(0 + 0) = 2 cis 20. State in your own words…

A: Given that: (rcisθ)2=(rcisθ)(rcisθ)=r2cis(θ+θ)=r2cis2θ

Q: Express 29 +11j -1+5j as a complex number in the form A + Bj. Further, move the red dot in the graph…

A:

Q: What can you say about z if |e|= 1. Ques

A: Note: Hi! Thank you for the question As per the honour code, We’ll answer the first question since…

Q: A complex number z satisfies arg z = 5. (a) Use a diagram to show that |z-2i| > 1. (b) For which…

A:

Q: In each part, find 121. 12. Z = -3 – 4i 13. z = -7i V3. 1 = Z 14.

A:

Q: The polar form of –256 – 256V3i is 512 (cos (-) + i sin (-)) (for steps, see polar form calculator).…

A:

Q: (cos20+i sin0) (cos30–i sin30)6 (cos40-i sin40)7(cos50–t sin50)8

A:

Q: Question 3 If z = a + bj, determine the equations of the loci and des (a) Izl = 2|2 - 41 %3D (b) arg…

A: Let z=a+bi. We have to find the loci and describe the given sets. a) z=2z-4 We know, z=a+bi=a2+b2…

Q: the complex number 6√3+6i in polar form 12(cos(n/6)+isin(n/6) 12(cos(n/4)+isin(n/4)…

A:

Q: For the numbers 2₁ = following questions: a) Note: you may enter your solution in various ways,…

A:

Q: 1. CS Three complex numbers are related as follows: MG=3+14 CM=5-12 Evaluated with CamScanner (a)…

A: Sol:- (a) To find CMG, we can simply multiply the given complex numbers:CMG = CM  MG  CG      =…

Q: (b) 3- 4i (c) V3 – i (d) –V6 – vZi (е)-81

A: for a complex number z = a+ib a = rcosθ , b = rsinθ r=|z|=a2+b2 θ=tan−1(ba) for a>-0θ=π−tan−1(ba)…

Q: 1. -5./20 2. (4 + Si )(4 – 5i) 3. (3– 2i)

A:

Q: QUESTION 6 Suppose z=2-3i , What is a complex function f (z) = – 37 – 2i Re (z) ? -6+13i 6+ 13i…

A: