Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation sin(x)=0
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Equation -7-x=3x+17
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Equation (7x+1)-(9x+4)=5
- Equation sin(x-0,5)=(|x^2-(0,5)^2(e)^x|)^(1/3)
- Express {x} in terms of y where:
- -9*x+12*y=-10
- -17*x-19*y=-18
- -14*x+11*y=20
- 11*x+10*y=17
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Identical expressions
- (three +2i)/(one -2i)=z
- (3 plus 2i) divide by (1 minus 2i) equally z
- (three plus 2i) divide by (one minus 2i) equally z
- 3+2i/1-2i=z
- (3+2i) divide by (1-2i)=z
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Similar expressions
- (3+2i)/(1+2i)=z
- (3-2i)/(1-2i)=z
(3+2i)/(1-2i)=z equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the linear equation:
Expand brackets in the left part
Looking for similar summands in the left part:
Move the summands with the unknown z
from the right part to the left part:
$$- z + \frac{\left(1 + 2 i\right) \left(3 + 2 i\right)}{5} = 0$$
Divide both parts of the equation by (-z + (1 + 2*i)*(3 + 2*i)/5)/z
We get the answer: z = -1/5 + 8*i/5
(3+2*i)/(1-2*i) = z
Expand brackets in the left part
3+2*i1-2*i = z
Looking for similar summands in the left part:
(1 + 2*i)*(3 + 2*i)/5 = z
Move the summands with the unknown z
from the right part to the left part:
$$- z + \frac{\left(1 + 2 i\right) \left(3 + 2 i\right)}{5} = 0$$
Divide both parts of the equation by (-z + (1 + 2*i)*(3 + 2*i)/5)/z
z = 0 / ((-z + (1 + 2*i)*(3 + 2*i)/5)/z)
We get the answer: z = -1/5 + 8*i/5
The graph
Rapid solution
[src]
1 8*I
z1 = - - + ---
5 5
$$z_{1} = - \frac{1}{5} + \frac{8 i}{5}$$
z1 = -1/5 + 8*i/5
Sum and product of roots
[src]
sum
1 8*I - - + --- 5 5
$$- \frac{1}{5} + \frac{8 i}{5}$$
=
1 8*I - - + --- 5 5
$$- \frac{1}{5} + \frac{8 i}{5}$$
product
1 8*I - - + --- 5 5
$$- \frac{1}{5} + \frac{8 i}{5}$$
=
1 8*I - - + --- 5 5
$$- \frac{1}{5} + \frac{8 i}{5}$$
-1/5 + 8*i/5