1. Fill in each blank so that the resulting statement is true. To convert a complex number from rectangular form, z = a + bi, to polar form, z=r( cos 0 + i sin ()), we use the relationships r= and tan 0 = noting the quadrant in which the graph of z lies. To convert a complex number from rectangular form, z = a + bi, to polar form, z= r( cos 0 + i sin 0)), we use the relationships r = (1) and tan 0 = (2) noting the quadrant in which the graph of z lies. (1) O (2) 0 Vaz + (bi)? Ova + (bi )? O O a 2 + b 2 O O O Va 2+ 622. Fill in each blank so that the resulting statement is true. 1 ( cos 0, + i sin @1 ) . 2 ( cos 02 + i sin 02) =_ [cos + i sin ( The product of two complex numbers in polar form is found by their moduli and their arguments. ry ( cos 0, + i sin 01 ) . 2 ( cos 02 + i sin 02) = (1) [cos (2) + i sin (3) The product of two complex numbers in polar form is found by (4) their moduli and (5) their arguments. (1) 1 (2) O (01 +02) (3) 0 (0 1 +02 ) (4 ) O adding (5) O multiplying O 12 O (01 -02) dividing O subtracting O subtracting O adding O O multiplying dividing O (1 1 + 12) 1 2 O (0102 ) O (1 1 -12) O (0,#2 ) O (0 1 - 02)3. Fill in each blank so that the resulting statement is true. 1 ( cos 0, + i sin 0, ) 2 ( cos 02 + i sin 02 ) [cos + i sin ( )] The quotient of two complex numbers in polar form is found by their moduli and their arguments. 1 ( cos 0, + i sin 01 ) 2 ( cos 02 + i sin 02) (1) [ cos (2) + i sin (3) The quotient of two complex numbers in polar form is found by (4). their moduli and (5) their arguments (1) 0 riz (2) O (01 -02) (3) O (01 -02 ) (4) O subtracting (5) O multiplying 1 O (0102 ) O adding O adding O O 12 O dividing O dividing O O multiplying O subtracting O (1 1 + 12) O (01 + 02) O (r1 - 12) O (0102) O (01 + 02) 4. Fill in each blank so that the resulting statement is true. DeMoivre's Theorem states that [r( cos 0 + i sin 0)]" = [ cos + i sin ()]. DeMoivre's Theorem states that [r( cos 0 + i sin 0)]" = (1)- [ cos (2) + i sin (3) -]. (1) O (n-1)0 (2) O [(n - 1)0] (3) 0 (r -1 ) O (7) [e(L - U)] O 0 7- 1 O (, -1 ) O (ne) O no O (ne)5. Plot the complex number and find its absolute value. Almaginary 6 1 Plot the complex number on the complex plane to the right. The absolute value of the complex number is Real (Simplify your answer. Type an exact answer, using radicals as needed.) https://xlitemprod.pearsonomg.com/api/v1/print/highered 2/6 10/19/22, 9:48 PM HwSec6.5-Adriana Lumbreras 6. Plot the complex number and find its absolute value. Almaginary 12 Plot the complex number on the complex plane to the right. What is the absolute value of this complex number? Real |12) = Simplify your answer. Type an exact answer, using radicals as needed.)6. Plot the complex number and nd its absolute value. 12 Plot the complex number on the complex plane to the right. What is the absolute value of this complex number? we: (Simplify your answer. Type an exact answer. using radicals as needed.) 7". Plot the complex number and find its absolute value. 12 E Plot the complex number on the complex plane to the right. The absolute value of the complex number is I12 ii = :- (Simplify your answer. Type an exact answer. using radicals as needed.) Imaginary Real 8. Plot the complex number and find its absolute value. A Imaginary -4-31 Plot the complex number on the complex plane to the right. The absolute value of the complex number is Real 1-4-31| = 20 416212 (Simplify your answer. Type an exact answer, using radicals as needed.)9. Plot the complex number and find its absolute value. magma\12. Find the product of the complex numbers. Leave your answer in polar form. 21 = or one 25 + i sin 25") 22 = 7( cos 15 + 5 sin 15") [Simplify your answer. Use integers or fractions for any numbers in the expression.) 13. Find zw. Leave your answer in polar form. 11: TI: 2:8 oos-+ isin B 5 1n: _ . TI! w2 605+ 1. 5mm (Reduce any fractions. Describe the angle using radians between D and 2a.) 14. Find the product of the complex numbers. Leave your answer in polar form. z1=5+5 2223+3i (Simplify your answer. Use integers or fractions for any numbers in the expression. Type any angles in radians between 0 and 21:. Express complex numbers in terms of i.) 15. Z1 Find the quotient z of the complex numbers. Leave your answer in polar form. 2 21 = 24(cos120 + i sin 120) 22 = ar cos 30 + i sin 30} (Simplify your answer. Use integers or fractions for any numbers in the expression.) 16. 21 Find the quotient : of the complex numbers. Leave your answer in polar form. 2 6 TI: . _ 1|: 7 1E _ _ 1'1: : + : + _ 21 cos 10 15m 10 22 c0511 ism11 7-1 (Simplify your answer. Use integers or fractions for any numbers in the expression. Type any angles in radians between 0 and 21:. Express complex numbers in terms of 1'.) 17. Use DeMoivre's Theorem to find the indicated power of the complex number. Write the answer in rectangular form. [4( cos 75 + i sin 750)]3 [4( cos 75 + i sin 75)13 = (Simplify your answer, including any radicals. Type your answer in the form a + bi. Use integers or fractions for any numbers in the expression. Rationalize all denominators.) 18. Use DeMoivre's Theorem to find the indicated power of the complex number. Write the answer in rectangular form. 2n 14 13 COS 3 + i sin 3 74 V3 cos 3 - + i sin 3 (Simplify your answer. Type an exact answer, using radicals and i as needed.)19. Use DeMoivre's Theorem to find the indicated power of the complex number. Write the answer in rectangular form. (v15 + iv/5) 2 (v15 + 1 15) 2 = (Simplify your answer. Type your answer in the form a + bi. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression. Rationalize all denominators.) 20. Use the Root-slider to select the 4th root, and move the red point to the complex number 0 + 4 i . Select the Show Values, Geometry, and Polar Form boxes. Use the interactive figure to find your answer. Use the left and right arrow keys to move along a slider as needed. Click here to launch the interactive figure.' (i) What is radius of each fourth root of 0 + 4 /? The radius of each fourth root of 0 + 4 / is (Type an integer or decimal rounded to one decimal place as needed.) (ii) What is the angle of the complex root with the smallest angle? The angle of the complex root with the smallest angle is (Type an integer or decimal rounded to one decimal place as needed.) (ii) Consecutive complex roots are separated by degrees. Consecutive complex roots are separated by degrees