x=((30)/(5.15+1.84i))+(5.15+1.84i)

i= square root of (-1)
final answer of x=10.3
please show me how you drive this equation to get the 10.3.
thank you so much.

very good, but when i want to proove it by x + y =10.3,

x=30/(5.15+1.84i), y=(5.15+1.84i)
how you drive this equation
30/(5.15+1.84i)+(5.15+1.84i)=10.3
thank you

http://www.jiskha.com/display.cgi?id=1285074559

See:

http://www.jiskha.com/display.cgi?id=1285095664

To find the final value of x, let's break down the equation step by step:

1. Start with the given equation: x = (30/(5.15+1.84i)) + (5.15+1.84i).

2. Simplify the expression within the parentheses first: 5.15 + 1.84i.

3. Next, calculate the value of the fraction 30/(5.15+1.84i).

4. To divide by a complex number, we multiply both the numerator and denominator by its conjugate, which is equal to the original complex number but with the opposite sign of the imaginary part.
Conjugate of (5.15+1.84i) = (5.15-1.84i).

5. Multiply the numerator and denominator of the fraction by the conjugate:
30 * (5.15-1.84i) / ((5.15+1.84i) * (5.15-1.84i)).

6. Simplify the denominator by using the FOIL method (First, Outer, Inner, Last):
((5.15+1.84i) * (5.15-1.84i)) = 5.15 * 5.15 + 5.15 * (-1.84i) + 1.84i * 5.15 + 1.84i * (-1.84i).

7. Continue simplifying:
(26.5225 + 9.466i - 9.466i + 3.3936) = 29.9155 + 0i.

8. Now substitute the simplified numerator and denominator back into the equation:
x = (30 * (5.15 - 1.84i)) / (29.9155 + 0i) + (5.15 + 1.84i).

9. Simplify the complex fraction by performing the multiplication:
30 * (5.15 - 1.84i) = 154.5 - 55.2i.

10. Substitute the numerator back into the equation:
x = (154.5 - 55.2i) / (29.9155 + 0i) + (5.15 + 1.84i).

11. Since there is no imaginary part in the denominator, we can multiply the numerator and denominator by the conjugate of the denominator, which is simply 29.9155:
((154.5 - 55.2i) / (29.9155 + 0i)) * (29.9155 / 29.9155).

12. Multiply and simplify:
(154.5 * 29.9155 - 55.2i * 29.9155) / (29.9155 * 29.9155).

13. Calculate the numerator:
(4627.18 - 1652.748i) / 895.1701025.

14. Divide both the real and imaginary parts of the numerator by the denominator:
4627.18 / 895.1701025 - (1652.748 / 895.1701025)i.

15. Calculate:
5.162707 - 1.844693i.

16. Finally, substitute back into the original equation:
x = 5.162707 - 1.844693i + (5.15 + 1.84i).

17. Combine the real parts and the imaginary parts separately:
x = (5.162707 + 5.15) + (-1.844693i + 1.84i).

18. Add the real and imaginary parts:
x = 10.312707 + (-0.004693i).

19. The final answer is x = 10.3 after rounding to one decimal place.