5-14 - A Complex Number and Its Modulus Graph the complexnumber and find its modulus.5. 4i6. -3i7. -28. 6. 9. 5 + 2i10. 7- 31-1-11. V3 + i12.3 + 4i13.14.52

Answered: 5-14 - A Complex Number and Its Modulus…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Plot the complex number. 2 - 2/3i Imaginary Imaginary axis axis 10- 10 2-2 V3 i Real Real -10 -5 10 ахis 10 -5 10 axis 2 - 2 V3 i -5 -5- -10 -10F
0-01 The value of (1)100 is equal to: (B) 1 (A) en/2 Given the two complex numbers: (A) 2+1 (B) 1+21 (C) e-** (D) -1 Z₁-1+1, 2,-1, the value of 2, + Z₂ is: (C) (D) 2+21 Q-03 Given the two complex numbers: Z₁ (A) 9 (B) 16 =3+41, Z₂-3-44, the value of Z, Z, in: (C) 25(D) 9-161
Graph the complex number. 2 + 4i -5 -4 -3 r = L Find the modulus r. Need Help? -3 -2 -1 -5-4-3 -3 -2 -1 L Read It Im -it Im -it Watch It L 1 2 L 1 L 2 L 3 4 3 J 4 4 5 5 Re Re -5 -4 -3 -2 -1 -5-4-3 -3 -2 -1 Im -1 Im -1 1 2 1 L 2 3 3 4 L 4 5 5 Re Re
(Review of Complex Numbers) The three most important facts to know about complex numbers are that • 12 = -1 • every complex number can be written in the form a + bi, where a and b are real numbers ⚫elt = cos(t)+isin(t) (this is known as Euler's formula) When manipulating complex numbers, you are free to always treat i as you would with normal algebra (in terms of factoring, rearranging, etc.). If you ever have an i², you can replace it with -1. To divide complex numbers, you can multiply a fraction's numerator and denominator by the complex conjugate of the denominator, and then simplify: a+bi a+bi c-di = c+di cdi cdi You should be able to rearrange it to something of the form A + Bi, where A and B are real numbers. Write each of the following numbers in the form a + bi, where a and b are real numbers. (a) (2+3)(2-3i) 2+3i (b) 2-i
2. Write the given complex numbers in the form a + bi. 3 (a) + - (b) 2;ª + ()" + 5i 5 - 12i (c) 2-4i 3+5i (d) (3-i)(2+3i) 1+i
Example-1. Express (1–2i)². Fin the form A+iB. Also find its modulas and (2+i)? argument. Example-2. Find the real and imaginary parts of 1+cos 0 +i sin and also find uts 1+cos Ø+i sin Ø modulas. Example-3. Find the modulas and argument of the following complex numbers 1-i (ii) -2 : (i) 1+iv3 1+i
(Review of Complex Numbers) The three most important facts to know about complex numbers are that • i² = -1 ⚫ every complex number can be written in the form a + bi, where a and b are real numbers ⚫eit = cos(t) + i sin(t) (this is known as Euler's formula) When manipulating complex numbers, you are free to always treat i as you would with normal algebra (in terms of factoring, rearranging, etc.). If you ever have an i², you can replace it with -1. To divide complex numbers, you can multiply a fraction's numerator and denominator by the complex conjugate of the denominator, and then simplify: a+bi = abic di c+ di c+ di c - di =... You should be able to rearrange it to something of the form A + Bi, where A and B are real numbers. Write each of the following numbers in the form a + bi, where a and b are real numbers. (c) iii2-i+1 (d) eлi

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5-14 - A Complex Number and Its Modulus Graph the complex number and find its modulus. 5. 4i 6. -3i 7. -2 8. 6 . 9. 5 + 2i 10. 7- 31 -1- 11. V3 + i 12. 3 + 4i 13. 14. 5 2