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cshum00

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## Homework Statement

Evaluate the following complex numbers (results in rectangular form):

[tex] \frac{10 + j5 + 3\angle 40^{\circ}}{-3 + j4} + 10 \angle 30^{\circ} [/tex]

## Homework Equations

I know that the solution is:

8.293 + j2.2

But i get a different answer.

## The Attempt at a Solution

Convert into rectangular form when adding or subtracting and to polar form when multiplying and dividing. Change the answer to rectangular form.

[tex] \frac{10 + j5 + 3\angle 40^{\circ}}{-3 + j4} + 10 \angle 30^{\circ} [/tex]

[tex] \frac{10 + j5 + 3cos(40^{\circ}) + 3jsin(40^{\circ})}{[(-3)^2 + (4)^2]^1^/^2 \angle arctan(4/-3)} + 10cos(30^{\circ}) + 10jsin(30^{\circ}) [/tex]

[tex] \frac{10 + j5 + 2.30 + j1.93}{5 \angle -53.13^{\circ}} + 8.66 + j5[/tex]

[tex] \frac{12.30 + j6.93}{5 \angle -53.13^{\circ}} + 8.66 + j5[/tex]

[tex] \frac{[(12.30)^2 + (6.93)^2]^1^/^2 \angle arctan(6.93/12.30)}{5 \angle -53.13^{\circ}} + 8.66 + j5[/tex]

[tex] \frac{14.12 \angle 29.40^{\circ}}{5 \angle -53.13^{\circ}} + 8.66 + j5[/tex]

[tex] \frac{14.12}{5}\angle [29.40^{\circ}-(-53.13^{\circ})] + 8.66 + j5[/tex]

[tex] 2.824 \angle 83.53^{\circ} + 8.66 + j5[/tex]

[tex] 0.37 + j2.8 + 8.66 + j5[/tex]

[tex] 9.03 + j7.8[/tex]

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