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

Question

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.

Answer 1

The trick is the first term, 30/(5.15+1.84i).

Multiply both numerator and denominator by the conjugate of the denominator, namely (5.15-1.84i) to get
30(5.15-1.84i)/(5.15²-(1.84i)²)
=30(5.15-1.84i)/(29.9)
=5.15-1.84i (approximately

So
((30)/(5.15+1.84i))+(5.15+1.84i)
=5.15-1.84i + 5.15+1.84i (approx.)
=10.3

Note the exact solution to the equations:
xy=30 and x+y=10.3 is
x=5.15±√(3.4775)
=5.15±1.8648 (approx.)