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

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

Guest May 6, 2015

#1
+26626
+10

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
Sort:

#1
+26626
+10

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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