Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation tan(x/3)+1=0
- Equation (-12*x-(-24)*y)-(-12*x+(-15)*y)=-51
- Equation (3x+5)-7=19
- Equation (-exp^(2x))-18*exp+9=-72
- Express {x} in terms of y where:
- -4*x-19*y=5
- -4*x-16*y=-2
- -10*x+2*y=16
- -13*x-8*y=-16
- Graphing y =:
- sinz
-
Identical expressions
- sinz= three + two *i
- sinus of z equally 3 plus 2 multiply by i
- sinus of z equally three plus two multiply by i
- sinz=3+2i
-
Similar expressions
- sin(z)-z+(z^3/(6))=0
- sin(z)=πi
- u=e^(x^3*y)*sin(z^2)
- -590*А*sin(z)+1284.849*A*cos(z)
- (3+2i)/(1-2i)=z
- sinz=3-2*i
sinz=3+2*i equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\sin{\left(z \right)} = 3 + 2 i$$
- 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.
$$\sin{\left(z \right)} = 3 + 2 i$$
- 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
Rapid solution
[src]
z1 = pi - re(asin(3 + 2*I)) - I*im(asin(3 + 2*I))
$$z_{1} = - \operatorname{re}{\left(\operatorname{asin}{\left(3 + 2 i \right)}\right)} + \pi - i \operatorname{im}{\left(\operatorname{asin}{\left(3 + 2 i \right)}\right)}$$
z2 = I*im(asin(3 + 2*I)) + re(asin(3 + 2*I))
$$z_{2} = \operatorname{re}{\left(\operatorname{asin}{\left(3 + 2 i \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(3 + 2 i \right)}\right)}$$
z2 = re(asin(3 + 2*i)) + i*im(asin(3 + 2*i))
Sum and product of roots
[src]
sum
pi - re(asin(3 + 2*I)) - I*im(asin(3 + 2*I)) + I*im(asin(3 + 2*I)) + re(asin(3 + 2*I))
$$\left(- \operatorname{re}{\left(\operatorname{asin}{\left(3 + 2 i \right)}\right)} + \pi - i \operatorname{im}{\left(\operatorname{asin}{\left(3 + 2 i \right)}\right)}\right) + \left(\operatorname{re}{\left(\operatorname{asin}{\left(3 + 2 i \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(3 + 2 i \right)}\right)}\right)$$
=
pi
$$\pi$$
product
(pi - re(asin(3 + 2*I)) - I*im(asin(3 + 2*I)))*(I*im(asin(3 + 2*I)) + re(asin(3 + 2*I)))
$$\left(\operatorname{re}{\left(\operatorname{asin}{\left(3 + 2 i \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(3 + 2 i \right)}\right)}\right) \left(- \operatorname{re}{\left(\operatorname{asin}{\left(3 + 2 i \right)}\right)} + \pi - i \operatorname{im}{\left(\operatorname{asin}{\left(3 + 2 i \right)}\right)}\right)$$
=
-(I*im(asin(3 + 2*I)) + re(asin(3 + 2*I)))*(-pi + I*im(asin(3 + 2*I)) + re(asin(3 + 2*I)))
$$- \left(\operatorname{re}{\left(\operatorname{asin}{\left(3 + 2 i \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(3 + 2 i \right)}\right)}\right) \left(- \pi + \operatorname{re}{\left(\operatorname{asin}{\left(3 + 2 i \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(3 + 2 i \right)}\right)}\right)$$
-(i*im(asin(3 + 2*i)) + re(asin(3 + 2*i)))*(-pi + i*im(asin(3 + 2*i)) + re(asin(3 + 2*i)))
Numerical answer
[src]
z1 = 46.1592312994393 - 1.9686379257931*i
z2 = -4.1062511579974 - 1.9686379257931*i
z3 = 96.424713756876 - 1.9686379257931*i
z4 = 33.5928606850801 - 1.9686379257931*i
z5 = 39.8760459922597 - 1.9686379257931*i
z6 = -49.3008239530291 + 1.9686379257931*i
z7 = 58.7256019137985 - 1.9686379257931*i
z8 = -43.0176386458495 + 1.9686379257931*i
z9 = 76.3628821905626 + 1.9686379257931*i
z10 = 108.991084371235 - 1.9686379257931*i
z11 = 0.964658504407603 + 1.9686379257931*i
z12 = 14.7433047635414 - 1.9686379257931*i
z13 = -48.0885483082545 - 1.9686379257931*i
z14 = -61.8671945673883 + 1.9686379257931*i
z15 = -35.5221776938953 - 1.9686379257931*i
z16 = 71.2919725281576 - 1.9686379257931*i
z17 = 83.8583431425168 - 1.9686379257931*i
z18 = -92.0708454585116 - 1.9686379257931*i
z19 = 13.5310291187668 + 1.9686379257931*i
z20 = 7.24784381158719 + 1.9686379257931*i
z21 = 51.2301409618443 + 1.9686379257931*i
z22 = -99.5663064104658 + 1.96863792579308*i
z23 = -55.5840092602087 + 1.9686379257931*i
z24 = 90.1415284496964 - 1.9686379257931*i
z25 = 44.9469556546647 + 1.9686379257931*i
z26 = -17.8848974171312 + 1.9686379257931*i
z27 = -60.6549189226137 - 1.9686379257931*i
z28 = 21.0264900707209 - 1.9686379257931*i
z29 = 57.5133262690239 + 1.9686379257931*i
z30 = -16.6726217723566 - 1.9686379257931*i
z31 = 27.3096753779005 - 1.9686379257931*i
z32 = -86.9999357961066 + 1.9686379257931*i
z33 = -29.2389923867157 - 1.9686379257931*i
z34 = -73.2212895369728 - 1.9686379257931*i
z35 = -104.637216072871 - 1.9686379257931*i
z36 = -98.3540307656912 - 1.9686379257931*i
z37 = -22.9558070795362 - 1.9686379257931*i
z38 = 101.495623419281 + 1.9686379257931*i
z39 = -66.9381042297933 - 1.9686379257931*i
z40 = 88.9292528049218 + 1.9686379257931*i
z41 = 77.5751578353372 - 1.9686379257931*i
z41 = 77.5751578353372 - 1.9686379257931*i