(a) Explanation Given: Complex numbers - z 1 = − 12 3 − 12 i ; z 2 = − 6 + 6 3 i Formula Used: Let two complex number z 1 and z 2 be as follows: z 1 = r 1 ( cos θ 1 + i sin θ 1 ) z 2 = r 2 ( cos θ 2 + i sin θ 2 ) Then, the product of complex numbers is given as z 1 z 2 = r 1 r 2 [ cos ( θ 1 + θ 2 ) + i sin ( θ 1 + θ 2 ) ] Calculation: Complex numbers are given as follows: z 1 = − 12 3 − 12 i z 2 = − 6 + 6 3 i Converting z 1 = − 12 3 − 12 i into polar form r 1 = ( − 12 3 ) 2 + ( − 12 ) 2 r 1 = 288 + 144 r 1 = 4 × 4 × 3 × 3 × 3 r 1 = 12 3 And tan θ 1 = − 12 − 12 3 tan θ 1 = 1 3 θ 1 = tan − 1 ( 1 3 ) θ lies in 3 r d quadrant θ 1 = π + π 6 = 6 π + π 6 = 7 π 6 Thus, polar form is z 1 = r 1 ( cos θ + 1 i sin θ 1 ) z 1 = 12 3 ( cos 7 π 6 + i sin 7 π 6 ) Now, converting z 2 = − 6 + 6 3 i into polar form r 2 = ( 6 ) 2 + ( 6 3 ) 2 r 2 = 36 + 108 r 2 = 144 r 2 = 12 And tan θ (b) To determine To find z 1 z 2 and write the quotient in polar form z 1 = − 12 3 − 12 i ; z 2 = − 6 + 6 3 i

16th Edition

ISBN: 9781259976612

Author: Miller

Publisher: MCG CUSTOM

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Chapter 8.3, Problem 41PE

(a)

To determine

To find z1z2 and write the product in polar form

z1=−123−12i;z2=−6+63i

(b)

To determine

To find z1z2 and write the quotient in polar form

z1=−123−12i;z2=−6+63i

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Chapter 8.3, Problem 40PE

Chapter 8.3, Problem 42PE

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Chapter 8 Solutions

COLLEGE ALG.+TRIG.(LL)-W/ACCESS>CUSTOM<

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Knowledge Booster

To find z 1 z 2 and write the product in polar form z 1 = − 12 3 − 12 i ; z 2 = − 6 + 6 3 i

Solution Summary: The author explains how two complex numbers are given as follows: lz_12=r

To find z1z2 and write the product in polar form

z1=−123−12i;z2=−6+63i

To find z1z2 and write the quotient in polar form

z1=−123−12i;z2=−6+63i

Want to see the full answer?

Chapter 8 Solutions

To find z 1 z 2 and write the product in polar form z 1 = − 12 3 − 12 i ; z 2 = − 6 + 6 3 i

Solution Summary: The author explains how two complex numbers are given as follows: lz_12=r

To find z1z2 and write the product in polar form z1=−123−12i;z2=−6+63i

To find z1z2 and write the quotient in polar form z1=−123−12i;z2=−6+63i

Want to see the full answer?

Chapter 8 Solutions

To find z1z2 and write the product in polar form

z1=−123−12i;z2=−6+63i

To find z1z2 and write the quotient in polar form

z1=−123−12i;z2=−6+63i