natie18
11.12.2020 •
Mathematics
The complex numbers z and w satisfy |z| = |w| = 1 and zw is not equal to -1.
(a) Prove that \overline{z} = {1}/{z} and \overline{w} = {1}/{w}.
(b) Prove that {z + w}/{zw + 1} is a real number.
Can you please explain in detail? I'm trying to understand this. Thank you for your time.
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Ответ:
Number of 50sen coins = 13
Step-by-step explanation:
Let the number of 50sen coins be = x
Let the number of 20sen coins be = y
Total coins = 20
x + y = 20 (i)
Value of 50sen coins = 0.50*x = 0.50x
Value of 20sen coins = 0.20 *y = 0.20y
Total value = RM 6.10
0.5x + 0.2y = 6.10 (ii)
Multiply (i) by (-0.5) and then add the equations. So, x will be eliminated and we can find the value of y
(i) * (-0.5) -0.5x - 0.5y = -10
(ii) 0.5x + 0.2y = 6.10 { add and now x will be eliminated}
- 0.3y = -3.90
Divide both sides by (-0.3)
y = -3.90/-0.3
y = 13
Plug in the value of y in equation (i)
x + 13 = 20
Subtract 13 from both sides
x = 20 -13
x = 7
Number of 50sen coins = 13