Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation sinx=1
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Equation cosx=1/2
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Equation sqrt(x)+1=x-1
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Equation (x^2-x-1)/(x^2-2*x)=0
- Express {x} in terms of y where:
- xy^1=y+x*sin(y/x)
- sqrt(x)*sin(y/x)=0
- 12*10^(-30)-0,1884*10^12*x^2-y(0,3768*10^12*x+1,183152*10^12*x^3)+y^2(2,760688*10^24*x^2)=0=0
- (x^2+y^2)×(x+y-3)=2xy
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Identical expressions
- z=(- one / two)+((sqrt3i)/ two)
- z equally ( minus 1 divide by 2) plus (( square root of 3i) divide by 2)
- z equally ( minus one divide by two) plus (( square root of 3i) divide by two)
- z=(-1/2)+((√3i)/2)
- z=-1/2+sqrt3i/2
- z=(-1 divide by 2)+((sqrt3i) divide by 2)
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Similar expressions
- z=(1/2)+((sqrt3i)/2)
- z=(-1/2)-((sqrt3i)/2)
z=(-1/2)+((sqrt3i)/2) equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
_____
1 \/ 3*I
z = - - + -------
2 2
$$z = - \frac{1}{2} + \frac{\sqrt{3 i}}{2}$$
Detail solution
Given the linear equation:
Expand brackets in the right part
We get the answer: z = -1/2 + sqrt(3)*sqrt(i)/2
z = (-1/2)+((sqrt(3*i))/2)
Expand brackets in the right part
z = -1/2+sqrt+3*i)/2)
We get the answer: z = -1/2 + sqrt(3)*sqrt(i)/2
The graph
Rapid solution
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___ ___
1 \/ 6 I*\/ 6
z1 = - - + ----- + -------
2 4 4
$$z_{1} = - \frac{1}{2} + \frac{\sqrt{6}}{4} + \frac{\sqrt{6} i}{4}$$
z1 = -1/2 + sqrt(6)/4 + sqrt(6)*i/4
Sum and product of roots
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sum
___ ___ 1 \/ 6 I*\/ 6 - - + ----- + ------- 2 4 4
$$- \frac{1}{2} + \frac{\sqrt{6}}{4} + \frac{\sqrt{6} i}{4}$$
=
___ ___ 1 \/ 6 I*\/ 6 - - + ----- + ------- 2 4 4
$$- \frac{1}{2} + \frac{\sqrt{6}}{4} + \frac{\sqrt{6} i}{4}$$
product
___ ___ 1 \/ 6 I*\/ 6 - - + ----- + ------- 2 4 4
$$- \frac{1}{2} + \frac{\sqrt{6}}{4} + \frac{\sqrt{6} i}{4}$$
=
___ ___ 1 \/ 6 I*\/ 6 - - + ----- + ------- 2 4 4
$$- \frac{1}{2} + \frac{\sqrt{6}}{4} + \frac{\sqrt{6} i}{4}$$
-1/2 + sqrt(6)/4 + i*sqrt(6)/4
Numerical answer
[src]
z1 = 0.112372435695795 + 0.612372435695794*i
z1 = 0.112372435695795 + 0.612372435695794*i