Mister Exam
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How to use it?
- Equation:
-
Equation (x-1)*(x^2+8*x+16)=6*(x+4)
-
Equation x^2+20*x+100=0
-
Equation 2x+1-20x+15=6x+4
- Equation x*(-1/5)+x^2=0
- Express {x} in terms of y where:
- 7*x+17*y=-13
- 10*x+19*y=-8
- -11*x-15*y=-5
- -2*x+8*y=-7
-
Identical expressions
- sin(z-i)=-4i/ three
- sinus of (z minus i) equally minus 4i divide by 3
- sinus of (z minus i) equally minus 4i divide by three
- sinz-i=-4i/3
- sin(z-i)=-4i divide by 3
-
Similar expressions
- sin(z-i)=+4i/3
- sin(z+i)=-4i/3
sin(z-i)=-4i/3 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
-4*I
sin(z - I) = ----
3
$$\sin{\left(z - i \right)} = \frac{\left(-1\right) 4 i}{3}$$
Detail solution
Given the equation
$$\sin{\left(z - i \right)} = \frac{\left(-1\right) 4 i}{3}$$
- this is the simplest trigonometric equation
As right part of the equation
modulo =
but sin
can no be more than 1 or less than -1
so the solution of the equation d'not exist.
$$\sin{\left(z - i \right)} = \frac{\left(-1\right) 4 i}{3}$$
- this is the simplest trigonometric equation
As right part of the equation
modulo =
True
but sin
can no be more than 1 or less than -1
so the solution of the equation d'not exist.
The graph
Sum and product of roots
[src]
sum
I*(1 - asinh(4/3)) + pi + I*(1 + asinh(4/3))
$$i \left(1 - \operatorname{asinh}{\left(\frac{4}{3} \right)}\right) + \left(\pi + i \left(1 + \operatorname{asinh}{\left(\frac{4}{3} \right)}\right)\right)$$
=
pi + I*(1 - asinh(4/3)) + I*(1 + asinh(4/3))
$$\pi + i \left(1 - \operatorname{asinh}{\left(\frac{4}{3} \right)}\right) + i \left(1 + \operatorname{asinh}{\left(\frac{4}{3} \right)}\right)$$
product
I*(1 - asinh(4/3))*(pi + I*(1 + asinh(4/3)))
$$i \left(1 - \operatorname{asinh}{\left(\frac{4}{3} \right)}\right) \left(\pi + i \left(1 + \operatorname{asinh}{\left(\frac{4}{3} \right)}\right)\right)$$
=
I*(1 - asinh(4/3))*(pi + I*(1 + asinh(4/3)))
$$i \left(1 - \operatorname{asinh}{\left(\frac{4}{3} \right)}\right) \left(\pi + i \left(1 + \operatorname{asinh}{\left(\frac{4}{3} \right)}\right)\right)$$
i*(1 - asinh(4/3))*(pi + i*(1 + asinh(4/3)))
Rapid solution
[src]
z1 = I*(1 - asinh(4/3))
$$z_{1} = i \left(1 - \operatorname{asinh}{\left(\frac{4}{3} \right)}\right)$$
z2 = pi + I*(1 + asinh(4/3))
$$z_{2} = \pi + i \left(1 + \operatorname{asinh}{\left(\frac{4}{3} \right)}\right)$$
z2 = pi + i*(1 + asinh(4/3))
Numerical answer
[src]
z1 = -100.530964914873 - 0.0986122886681097*i
z2 = 3.14159265358979 + 2.09861228866811*i
z3 = 25.1327412287183 - 0.0986122886681097*i
z4 = -94.2477796076938 - 0.0986122886681097*i
z5 = -18.8495559215388 - 0.0986122886681097*i
z6 = -47.1238898038469 + 2.09861228866811*i
z7 = 15.707963267949 + 2.09861228866811*i
z8 = -75.398223686155 - 0.0986122886681097*i
z9 = -62.8318530717959 - 0.0986122886681097*i
z10 = -87.9645943005142 - 0.0986122886681097*i
z11 = 31.4159265358979 - 0.0986122886681097*i
z12 = 12.5663706143592 - 0.0986122886681097*i
z13 = 43.9822971502571 - 0.0986122886681097*i
z14 = 87.9645943005142 - 0.0986122886681097*i
z15 = 9.42477796076938 + 2.09861228866811*i
z16 = 21.9911485751286 + 2.09861228866811*i
z17 = 47.1238898038469 + 2.09861228866811*i
z18 = -15.707963267949 + 2.09861228866811*i
z19 = 84.8230016469244 + 2.09861228866811*i
z20 = 6.28318530717959 - 0.0986122886681097*i
z21 = -40.8407044966673 + 2.09861228866811*i
z22 = -78.5398163397448 + 2.09861228866811*i
z23 = -84.8230016469244 + 2.09861228866811*i
z24 = -31.4159265358979 - 0.0986122886681097*i
z25 = 97.3893722612836 + 2.09861228866811*i
z26 = -50.2654824574367 - 0.0986122886681097*i
z27 = 37.6991118430775 - 0.0986122886681097*i
z28 = 94.2477796076938 - 0.0986122886681097*i
z29 = -65.9734457253857 + 2.09861228866811*i
z30 = 69.1150383789755 - 0.0986122886681097*i
z31 = -81.6814089933346 - 0.0986122886681097*i
z32 = 78.5398163397448 + 2.09861228866811*i
z33 = -28.2743338823081 + 2.09861228866811*i
z34 = 72.2566310325652 + 2.09861228866811*i
z35 = -6.28318530717959 - 0.0986122886681097*i
z36 = -25.1327412287183 - 0.0986122886681097*i
z37 = 81.6814089933346 - 0.0986122886681097*i
z38 = -56.5486677646163 - 0.0986122886681097*i
z39 = 40.8407044966673 + 2.09861228866811*i
z40 = 56.5486677646163 - 0.0986122886681097*i
z41 = -37.6991118430775 - 0.0986122886681097*i
z42 = 62.8318530717959 - 0.0986122886681097*i
z43 = -69.1150383789755 - 0.0986122886681097*i
z44 = 91.106186954104 + 2.09861228866811*i
z45 = -21.9911485751286 + 2.09861228866811*i
z46 = 18.8495559215388 - 0.0986122886681097*i
z47 = -72.2566310325652 + 2.09861228866811*i
z48 = 59.6902604182061 + 2.09861228866811*i
z49 = -91.106186954104 + 2.09861228866811*i
z50 = -43.9822971502571 - 0.0986122886681097*i
z51 = 50.2654824574367 - 0.0986122886681097*i
z52 = -12.5663706143592 - 0.0986122886681097*i
z53 = -3.14159265358979 + 2.09861228866811*i
z54 = -0.0986122886681097*i
z55 = 75.398223686155 - 0.0986122886681097*i
z56 = 65.9734457253857 + 2.09861228866811*i
z57 = -97.3893722612836 + 2.09861228866811*i
z58 = -34.5575191894877 + 2.09861228866811*i
z59 = 28.2743338823081 + 2.09861228866811*i
z60 = -9.42477796076938 + 2.09861228866811*i
z61 = 100.530964914873 - 0.0986122886681097*i
z62 = 53.4070751110265 + 2.09861228866811*i
z63 = -53.4070751110265 + 2.09861228866811*i
z64 = -59.6902604182061 + 2.09861228866811*i
z65 = 34.5575191894877 + 2.09861228866811*i
z65 = 34.5575191894877 + 2.09861228866811*i