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Write the complex number z = 3 - 3?3 i in trigonometric form (sometimes called polar form). Express the angle ? in radians, where 0 ? ? < 2?. z = [ ](cos [ ] + i sin [ ])

          Write the complex number z = 3 - 3?3 i in trigonometric form (sometimes called polar form).
Express the angle ? in radians, where 0 ? ? < 2?.
z = [ ](cos [ ] + i sin [ ])
        
Write the complex number z = 3 - 3?3 i in trigonometric form (sometimes called polar form).
Express the angle ? in radians, where 0 ? ? < 2?.
z = [ ](cos [ ] + i sin [ ])

Added by Marilyn S.

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Introductory and Intermediate Algebra for College Students 4th
Introductory and Intermediate Algebra for College Students 4th
Robert Blitzer 4th Edition
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Write the complex number z = 3 - 3√3 i in trigonometric form (sometimes called polar form). Express the angle θ in radians, where 0 ≤ θ < 2π.
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Transcript

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00:01 So a complex number is given in cartesian coordinate in a complex number is given and we need to convert or we need to convert in this complex number in technometric form or in it is also known as a polar form.
00:18 So the complex number is given as that is equals to 3 minus 3 root 3 j.
00:24 Z is equal to three three root three sorry this is i this is i i i is called is a whose value is root of minus one so now i can write z as z is equal to taking three common so i can add one minus root three i now multiplying and dividing z by uh dividing z by one square plus root three square upon root of 1 square plus root 3 square.
01:01 So this is equals to 3 into root of 4 and bracket 1 upon root of 4 minus root 3 upon 4 i.
01:17 So this is equal to 3 to 6, 6 upon 1 upon 2 minus root 3 upon 2 iota.
01:23 So now, so we need to represent this as, so cost theta is equals to 1 by 2.
01:35 Then theta can, theta, theta belongs to 0 to 2 pi, so theta can be, so theta can be pi by 3 or 2 pi minus 5 by 3.
01:54 So that is, so theta for cost theta equal to half, theta, can be pi by 3 or it can be 5 pi by 3.
02:04 So these two values can be cost data.
02:07 And sine theta, sine theta is equals to minus root 3 by 2.
02:13 So sign theta is equal to minus root 3 by 2.
02:16 Then theta would be equals to, then theta will equals to pi, pi plus pi by 3...
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