Questions in polar and rectangular i want help

[r-soy]

Hi



I want check my answer if correct or not



write in rectangular form

1) Z2 = 3e^(-60)i

2) z3 = 7.19e^-2.13i

3) z1 = root2 e^(-pi/2)i

4)z2 = 3e^120i

5 ) z3 = 6.49e^-2.08i

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my answer :







1)

= 3{cos (-60 ) + i sin ( -60) }

= 3(cos(1/2) + i sin (-root 3/2 ) }

= 3(1/2 + - root3/2)

= 1/2 + - root 3 /6



2 )

= 7.19 { cos ( -2.13 ) - i sin (-2.13 ) }

= 7.19{ 0.999 - -(0.037 ) }

= 7.182 - 0.266



3 )



= root2 { cos (-pi/2) - i sin (-pi / 2 ) }

= root 2 ( 0- 1 )

= 0 - root2



4 )



= 3{ cos (120) - i sin (120) }

3(1/2) - ( root 3 /2 )

= 1/2 - root3/6



5 )

6.49 {(cos ( -2.08 ) - i sin ( -2.08 ) i )

= 6.49 (0.999 ) - ( -0.036 )

= 6.18 + -236

=6.18 - 236

 

[LCKurtz]

Hi
I want check my answer if correct or not

write in rectangular form

1) Z2 = 3e^(-60)i

I will help you on the first one. The first nitpick is that the exponential should be expressed in radian measure.

Z_2 =3e^{-\frac {i\pi}{3}}

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my answer :

1)

= 3{cos (-60 ) + i sin ( -60) }

= 3(cos(1/2) + i sin (-root 3/2 ) }

That step is wrong, cos(-60) isn't equal cos(1/2)...

= 3(1/2 + - root3/2)

which you now sort of fixed...

= 1/2 + - root 3 /6

and messed up again. What happened to the 3? The cosine of -60 degrees has one value and you have to choose the correct + or -.