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# Given z1 = -3 + 3i and z2 = 6cos150 + 6isin150, can you help me to explain why z 1 = z 2 ?

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Given z1 = -3  + 3i and z2 = 6cos150° + 6isin150°, can you help me to explain why z1 = z2 ?

Mar 2, 2019

#1
+23636
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Is that supposed to be    150 ?

I think

Given

-3 +3i          it should be       4.24 cos 135   + i 4.24 sin 135      DO you have some numbers incorrect?

Given   -3 sqrt(3)  + 3 i                   |z| = r =sqrt [ (-3sqrt3)^2   + 3^2 ]  = 6

then   6 cos 150 = -3 sqrt3      and    6i sin 150 = 3i      SO the points are the same on the graph.....

Mar 2, 2019
edited by ElectricPavlov  Mar 2, 2019
edited by ElectricPavlov  Mar 2, 2019
edited by ElectricPavlov  Mar 2, 2019

#1
+23636
0

Is that supposed to be    150 ?

I think

Given

-3 +3i          it should be       4.24 cos 135   + i 4.24 sin 135      DO you have some numbers incorrect?

Given   -3 sqrt(3)  + 3 i                   |z| = r =sqrt [ (-3sqrt3)^2   + 3^2 ]  = 6

then   6 cos 150 = -3 sqrt3      and    6i sin 150 = 3i      SO the points are the same on the graph.....

ElectricPavlov Mar 2, 2019
edited by ElectricPavlov  Mar 2, 2019
edited by ElectricPavlov  Mar 2, 2019
edited by ElectricPavlov  Mar 2, 2019