Mister Exam
Factor polynomial e^j120*6+e^j240*10+10
The solution
You have entered
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j120 j240 E *6 + E *10 + 10
$$\left(6 e^{j_{120}} + 10 e^{j_{240}}\right) + 10$$
E^j120*6 + E^j240*10 + 10
General simplification
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j120 j240 10 + 6*e + 10*e
$$6 e^{j_{120}} + 10 e^{j_{240}} + 10$$
10 + 6*exp(j120) + 10*exp(j240)
Numerical answer
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10.0 + 6.0*2.71828182845905^j120 + 10.0*2.71828182845905^j240
10.0 + 6.0*2.71828182845905^j120 + 10.0*2.71828182845905^j240
Combinatorics
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j120 j240 10 + 6*e + 10*e
$$6 e^{j_{120}} + 10 e^{j_{240}} + 10$$
10 + 6*exp(j120) + 10*exp(j240)
Assemble expression
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j120 j240 10 + 6*e + 10*e
$$6 e^{j_{120}} + 10 e^{j_{240}} + 10$$
10 + 6*exp(j120) + 10*exp(j240)
Rational denominator
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j120 j240 10 + 6*e + 10*e
$$6 e^{j_{120}} + 10 e^{j_{240}} + 10$$
10 + 6*exp(j120) + 10*exp(j240)
Combining rational expressions
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/ j120 j240\ 2*\5 + 3*e + 5*e /
$$2 \left(3 e^{j_{120}} + 5 e^{j_{240}} + 5\right)$$
2*(5 + 3*exp(j120) + 5*exp(j240))
Common denominator
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j120 j240 10 + 6*e + 10*e
$$6 e^{j_{120}} + 10 e^{j_{240}} + 10$$
10 + 6*exp(j120) + 10*exp(j240)
Trigonometric part
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j120 j240 10 + 6*(cosh(1) + sinh(1)) + 10*(cosh(1) + sinh(1))
$$6 \left(\sinh{\left(1 \right)} + \cosh{\left(1 \right)}\right)^{j_{120}} + 10 \left(\sinh{\left(1 \right)} + \cosh{\left(1 \right)}\right)^{j_{240}} + 10$$
10 + 6*cosh(j120) + 6*sinh(j120) + 10*cosh(j240) + 10*sinh(j240)
$$6 \sinh{\left(j_{120} \right)} + 10 \sinh{\left(j_{240} \right)} + 6 \cosh{\left(j_{120} \right)} + 10 \cosh{\left(j_{240} \right)} + 10$$
j120 j240 10 + 6*e + 10*e
$$6 e^{j_{120}} + 10 e^{j_{240}} + 10$$
10 + 6*exp(j120) + 10*exp(j240)
Powers
[src]
j120 j240 10 + 6*e + 10*e
$$6 e^{j_{120}} + 10 e^{j_{240}} + 10$$
10 + 6*exp(j120) + 10*exp(j240)