8:18 AM G0 +234 901 970 2349 August 15, 8:59 AM +94 UNIVERSITY OF ABUJA Faculty of Engineering B.Eng. (Chemical Engineering) CA Test FEG 221: Engineering Mathematics 11 Instruction Attempt all questions Second Semester 2022/2023 Session Date: 16 November 2023 Time allowed: 30 min 1. Given that represents the imaginary uni" for a complex number, what is the value of (1 mark) 2.Sich the amphical representation (Argand diagram) of 5- For vector -[3,0,4], find the Lach of the vector marks) (2 marks) (2 marks) H Unit vector in the direction P @marks) What is the cross product of vector(s) a-13-14) and 5-12.5.1) marks) 5. Given that U= If cosx- (2-2) (28-2) write the first four (4) terms of the series (4 marks) (Note: 01-1) , estimate cos 60", using the first four (4) terms of the series ||| = о marks) U ۲۲ 《

Q: Multiply complex numbers 3(cis122)4(cis213)

A: Given complex numbers: 3(cis122)4(cis213)

Q: #4. Show that equation | 2-1-2|=1 Can be written as 121²2 Re Z-2 Im Z +1=0.

A: Given equation  z-1-i  =1. Show that: z2 -2 Rez -2 Imz +1=0.

Q: 10 2) z = (-j)()

A: We have to use De Moivre's theorem cosθ+jsinθn=cosnθ+jsinnθ and Eular form of complex number…

Q: 7-i/-i divide complex number

A: Given : 7-ii

Q: Determine the imaginary part

A: In this question, we have to find the imaginary part of the given complex number.

Q: A complex numbers is a symbol x + jy, where x and y are = -1. numbers and i^2 rational O real O…

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Q: Evaluate log 1, log(-1), log i and log(-i) in the complex number filed.

A: Complex logarithmic function is defined as  logz=logz+i·Argz where z is complex number and z is…

Q: Acceptedcharacters:numbers, decimal point markers (period or comma), sign indicators (-),spaces…

A: It is given that  Number of times a coin tossed n = 7

Q: Divide. -2i 2+3i Write your answer as a complex number in standard form.

A: The given complex number division -2i2+3i. We have write the number in standard form.

Q: #6. Find the square roots of (a) 2i; (b) 1-√3 i and express them in rectangular wordinates. #7. Find…

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Q: Write all values of a) ln(e-2)   b) ln(-3)

A: In this solution, we will find the values: (a) lne-2 and (b) ln-3. We know that lnab=blna. We know…

Q: How many complex numbers z with |2| = katisfies the equation 2 %3D

A: z=1⇒z2=1⇒zz¯=1⇒z¯=1z

Q: Write the expression as a complex number in standard form. I) (-8 + 8i) – (2 + 4i) 2) (8i) + (-4 -…

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Q: Evaluate (3 – 4i)'

A: To evaluate the below complex number. 3−4ii

Q: Present complex number z in algebraic form =* + 23D 35 1-3i

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Q: 1 - 3i З 1 + 2i

A: To simplify the following expression.

Q: 6. Simplify: i72 a. i b. -1 C. -i d. 1 7. Multiply: (2- i)(4 + 3i)

A:

Q: 41^2=9^2+b^2 solving for the adjacent side of a right triangle  I got this: 1681=81+b^2 Now I'm…

A: SOLUTION-

Q: 12) (3 + 2i) + (5-3i) 13) (4 + 2i) (3 - 2i)

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Q: 5. Solve your given pair of complex numbers placing them on an Argand diagram. (a) X+Y (b) Y-X A =…

A: We have to solve the given pair of complex number and place them in argand diagramNote: According to…

Q: Directions: Complete this page with your teacher and partner. Solution in Standard Solution in…

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Q: a

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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: Acceptedcharacters:numbers, decimal point markers (period or comma), sign indicators (-),spaces…

A: Given: The distribution of X is as follows x P (X = x) 0 0.24 1 0.31 2 0.45