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1. Express the followings in the form of x + iy where r, y E R.(choose one.) (a) 금+ 부 (b) ( + ) ( – i)

1. Express the followings in the form of x + iy where r, y E R.(choose one.) (a) 금+ 부 (b) ( + ) ( – i)

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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1. Express the followings in the form of x + iy where r, y E R.(choose one.) (a) +부 (b) ( + ) ( – ) 2. Represent z = 3 – 3i in polar form. 3. Compute |(1+ i)(1 – i)(1+3i)| . 4. (choose one.) (a) Find all 3rd roots of -8i. (b) Find all complex roots of the equation 26 = -9 5. Find the principal argument and exponential form of (choose one.) (a) z = (b) z = v3+i (c) z = 2 – i !! 6. Solve the following equations for z.(choose one.) (a) (2+ 3i)z = (2 – i)z – i (b) iz + 2i = 4 7. Show the following limits (choose one.) (a) lim; 12: = 00 (az+b)a (b) lim,--0 ed = 5, if c 0. 8. Compute lim, -o m, if exists. Im(2 +0
Transcribed Image Text:1. Express the followings in the form of x + iy where r, y E R.(choose one.) (a) +부 (b) ( + ) ( – ) 2. Represent z = 3 – 3i in polar form. 3. Compute |(1+ i)(1 – i)(1+3i)| . 4. (choose one.) (a) Find all 3rd roots of -8i. (b) Find all complex roots of the equation 26 = -9 5. Find the principal argument and exponential form of (choose one.) (a) z = (b) z = v3+i (c) z = 2 – i !! 6. Solve the following equations for z.(choose one.) (a) (2+ 3i)z = (2 – i)z – i (b) iz + 2i = 4 7. Show the following limits (choose one.) (a) lim; 12: = 00 (az+b)a (b) lim,--0 ed = 5, if c 0. 8. Compute lim, -o m, if exists. Im(2 +0
9. Find f'(2) when (choose one.) (a) f(2) = z2 – 4z + 2 (b) f(2) = (1 – 2²)ª (c) f(2) = e'/÷, (2 # 0) 10. Let z = 1+ iy. Determine whether f(2) is entire function or not? (Hint: Use Cauchy- Riemann equations) f(2) = HE
Transcribed Image Text:9. Find f'(2) when (choose one.) (a) f(2) = z2 – 4z + 2 (b) f(2) = (1 – 2²)ª (c) f(2) = e'/÷, (2 # 0) 10. Let z = 1+ iy. Determine whether f(2) is entire function or not? (Hint: Use Cauchy- Riemann equations) f(2) = HE
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