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Записать число в трех формах Z=4/1+i*корень из 3

 May 6, 2015

Best Answer 

 #1
avatar+27549 
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I think this is asking for 3 ways of writing z = 4/(1+i√3)

 

1.  Multiply numerator and denominator by 1 - i√3:   4(1 - i√3)/(1+3), so z = 1 - i√3

 

2. |z| = √(1+3) = 2,  tan-1(-√3/1) = -pi/3:  z = 2e-i*pi/3

 

3. e = cos(θ) + i*sin(θ), so z = 2cos(pi/3) - 2i*sin(pi/3)

 

.

 May 6, 2015
 #1
avatar+27549 
+10
Best Answer

I think this is asking for 3 ways of writing z = 4/(1+i√3)

 

1.  Multiply numerator and denominator by 1 - i√3:   4(1 - i√3)/(1+3), so z = 1 - i√3

 

2. |z| = √(1+3) = 2,  tan-1(-√3/1) = -pi/3:  z = 2e-i*pi/3

 

3. e = cos(θ) + i*sin(θ), so z = 2cos(pi/3) - 2i*sin(pi/3)

 

.

Alan May 6, 2015

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