Cyan M

24 Juni 2024 05:33

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Cyan M

24 Juni 2024 05:33

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Tjendana T

Community

24 Juni 2024 07:22

Jawaban terverifikasi

<p>Jawaban &nbsp;<strong>D. ½</strong></p><p>&nbsp;</p><p><strong>Pembahasan&nbsp;</strong></p><p>Materi : Bilangan Kompleks</p><p>Konsep persamaan kuadrat&nbsp;</p><p>&nbsp;</p><p>Re(z) - Im(z) = 3</p><p>&lt;=&gt; [Re(z) - Im(z)]² = 3²</p><p>&lt;=&gt; (Re(z))² + (Im(z))² - 2.Re(z).Im(z) = 9</p><p>&lt;=&gt; 45 - 2.Re(z).Im(z) = 9</p><p>&lt;=&gt; 2.Re(z).Im(z) = 36</p><p>&lt;=&gt; Re(z).Im(z) = 18</p><p>&nbsp;</p><p>Mari disederhanakan persamaan yg ada,</p><p>a = Re(z) dan b = Im(z)&nbsp;</p><p>Re(z) - Im(z) = 3 ——&gt; &nbsp;a - b = 3</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &lt;=&gt; a = 3 + b</p><p>Re(z).Im(z) = 9 ——&gt; a.b = 18</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &lt;=&gt; (3 + b). b = 18</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &lt;=&gt; b² + 3b - 18 = 0</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &lt;=&gt; (b + 6)(b - 3) = 0</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &lt;=&gt; b = - 6 atau b = 3</p><p>&nbsp;</p><p>Bila b = -6 maka&nbsp;</p><p>a = 3 + (-6) = -3 ❌ krn ada syarat bahwa a, Re(z) &gt; 0</p><p>sehingga</p><p>nilai b, Im(z) = 3 dan a, Re(z) = 6</p><p>&nbsp;</p><p>Im(z)/Re(z) = 3/6</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = ½</p><p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p>

Jawaban  D. ½

 

Pembahasan 

Materi : Bilangan Kompleks

Konsep persamaan kuadrat 

 

Re(z) - Im(z) = 3

<=> [Re(z) - Im(z)]² = 3²

<=> (Re(z))² + (Im(z))² - 2.Re(z).Im(z) = 9

<=> 45 - 2.Re(z).Im(z) = 9

<=> 2.Re(z).Im(z) = 36

<=> Re(z).Im(z) = 18

 

Mari disederhanakan persamaan yg ada,

a = Re(z) dan b = Im(z) 

Re(z) - Im(z) = 3 ——>  a - b = 3

                                    <=> a = 3 + b

Re(z).Im(z) = 9 ——> a.b = 18

                          <=> (3 + b). b = 18

                          <=> b² + 3b - 18 = 0

                          <=> (b + 6)(b - 3) = 0

                          <=> b = - 6 atau b = 3

 

Bila b = -6 maka 

a = 3 + (-6) = -3 ❌ krn ada syarat bahwa a, Re(z) > 0

sehingga

nilai b, Im(z) = 3 dan a, Re(z) = 6

 

Im(z)/Re(z) = 3/6

                      = ½

 

 

 

 

 

 


Zeklin I

25 Juni 2024 12:57

I'm(z) Re(z) adalah Reza=re I'm=so Reza=maafkanlah I'm=sorry

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