(a) Explanation Given: Complex numbers - z 1 = − 5 − 5 i ; z 2 = 10 + 10 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 = − 5 − 5 i z 2 = 10 + 10 i Converting z 1 = − 5 − 5 i into polar form r 1 = ( − 5 ) 2 + ( − 5 ) 2 r 1 = 25 + 25 r 1 = 50 r 1 = 5 2 And tan θ 1 = − 5 − 5 tan θ 1 = 1 θ 1 = tan − 1 ( 1 ) θ lies in 3 r d quadrant θ 1 = π + π 4 = 4 π + π 4 = 5 π 4 Thus, polar form is z 1 = r 1 ( cos θ + 1 i sin θ 1 ) z 1 = 5 2 ( cos 5 π 4 + i sin 5 π 4 ) Now, converting z 2 = 10 + 10 i into polar form r 2 = ( 10 ) 2 + ( 10 ) 2 r 2 = 100 + 100 r 2 = 200 r 2 = 1 (b) To determine To find z 1 z 2 and write the quotient in polar form z 1 = − 5 − 5 i ; z 2 = 10 + 10 i

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ISBN: 9781265934590

Author: Miller

Publisher: MCG CUSTOM

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Chapter 8.3, Problem 40PE

(a)

To determine

To find z1z2 and write the product in polar form

z1=−5−5i;z2=10+10i

(b)

To determine

To find z1z2 and write the quotient in polar form

z1=−5−5i;z2=10+10i

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Chapter 8.3, Problem 39PE

Chapter 8.3, Problem 41PE

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To find z 1 z 2 and write the product in polar form z 1 = − 5 − 5 i ; z 2 = 10 + 10 i

Solution Summary: The author explains how to convert complex numbers into a polar form.

Videos

To find z1z2 and write the product in polar form

z1=−5−5i;z2=10+10i

To find z1z2 and write the quotient in polar form

z1=−5−5i;z2=10+10i

Want to see the full answer?

Chapter 8 Solutions

To find z 1 z 2 and write the product in polar form z 1 = − 5 − 5 i ; z 2 = 10 + 10 i

Solution Summary: The author explains how to convert complex numbers into a polar form.

Videos

To find z1z2 and write the product in polar form z1=−5−5i;z2=10+10i

To find z1z2 and write the quotient in polar form z1=−5−5i;z2=10+10i

Want to see the full answer?

Chapter 8 Solutions

To find z1z2 and write the product in polar form

z1=−5−5i;z2=10+10i

To find z1z2 and write the quotient in polar form

z1=−5−5i;z2=10+10i