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: The ground rent was set at £28 per year for the first 21 years of the lease, increasing by £14 to…

A: a) The number of the 21-year period in 999 years is the quotient of 99921. Which is 47.…

Q: 1. Consider the nonzero complex numbers z1 = 3i, z2 = 6i and z3 = 4i. (a) Evaluate (z,z,z3) (1 + z2…

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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: (i) Evaluate the complex number (a+bi)4n+2 + (b − ai) 4n+2 where n is any positive integer. (ii)…

A: This is a problem of complex analysis.

Q: iree complex Z1 = 1- 2i, z2 = 6i, z2 = -3 -i. Compute the following, with your answer expressed in…

A: given that z1=1-2i,z2=6i,z3=-3-i find a)z1+z2z3b)3z2*-4z1z1c)z1z2*-3iz3

Q: 37. For the complex numbers (a) Arg(212) Arg(z1) (b) Arg(z1/22) Arg(z1 38. For the complex numbers…

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Q: 13. Use the exponential form of a complex number to write a + ib. ++) in the form

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Q: Express the complex numbers in the form x + iy. Show all your work and please answer a, b, & c as…

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

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Q: roblems 1. 2

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Q: -following expression as a complex number in polar form = evi = + + 8-j6 J² magnitude 1 phase = 14°…

A: The complex numbers are given in the polar coordinates.The aim is to digitalize the given content.

Q: 6. Find the following complex numbers in the form r+ iy, whe and y are real. (i) (3+7i) + (6 – 10i)…

A: we have to find complex numbers in the form of x + i y  Adding real part with real part and…

Q: 1) If we have the following complex numbers: Z, =2+3i, Z, =3-2i %3D Z, (d) Find (a) Z, + Z2 (b) Z,…

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Q: Simplify (4 + 2i) +(-3- 5i) Answers must be in simplified radical form. No decimal approxin given…

A: Let y=(4+2i)+(-3-5i)

Q: 1. Solve the following equations. a) (7+2/)+(4-3) b) (5-2/ (2-)(4+2) d) 2- 1+2 e) 21-3 2. Find x in…

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

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Q: (d) Let Z₁ = −4+ 8i and Z₂ = -1 -2i. Show that (i) 21/2₂ | = 4. | (ii) (iii) |z₁|² +Z₁ Z₂ = 100.…

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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: Write each of the complex numbers in the form a + iß, where a and B are real numbers. (a) 2ei/3 (b)…

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Q: 20. Express (-3 - 8i) (-7 + 2i) + (7 - 3i) in simplest a + bi form

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Q: 40 + 70j + j100 tan 0.67 = 100 100 + j(40 + 70j) tan 0.67 40–237.8j 40 + 70j + j100 × (-3.078) = 100…

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

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Q: Find the complex numbers in the form of z = a + bi such that zz*= 100 and a+b= 14. Note: answers…

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Q: How did it became -2pi/27 from the equation (-2pi/3+2pi(0))/9? Please explain.

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Q: 2. Express the following complex numbers in the form a + bi: (a) (2+3i)(4+i) (b) (8+6)² (c) (1 + ₁…

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

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Q: Assuming either 121=1 Prove that Z-W 1-ZW or /w/=1 and Zw=1. = 1.

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Q: 2.21 Consider the calculations of complex numbers C. (a) Let z = 2 - 3i and w = -1 + i. Determine…

A: Substitute the value of z and w in zw and multiple the complex numbers using the distributive…