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tatyana61 [14]
3 years ago
5

Complex numbers are used in electronics to describe the current in an electric circuit. Ohm's law relates the current in a circu

it, I, in amperes, the voltage of the circuit, E, in volts, and the resistance of the circuit, R, in ohms, by the formula Solve the problem using this formula. Find E, the voltage of a circuit, if I = (16 + i) amperes and R = (2 + 4i) ohms.
Mathematics
1 answer:
nekit [7.7K]3 years ago
6 0

Answer:

E = (28 + 66i) Volts

Step-by-step explanation:

Note that: i = √-1 ; i² = -1

Ohm's law: E = IR

E = (16+ i) (2 + 4i)

Expand the equation.

E = 16x2 + 16x4i + ix2 + ix4i

E = 32 + 64i + 2i + 4i²

E = 32 + 64i + 2i + 4(-1)

E = 32 + 64i + 2i - 4

Collect like terms:

E = 32 -4 + 64i + 2i

E = (28 + 66i) Volts

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What values of x make the equation x2 + 9x – 22 = 0 true? Check all that apply. –11 –2 0 2 11
Marat540 [252]
Answer:  x = 2 ;  -11 .
___________________________________
Explanation:
_____________________________________________
Given the equation:
_____________________________________________
  x² + 9x −<span> 22 = 0  ;  Solve for:  "x" ;
_____________________________________________

Let us factor the "left-hand side" of the equation:
_____________________________________________
  "x</span>² + 9x −<span> 22"  ;
_____________________________________________

What are the factors of "-22"" that add up to "positive 9" ?
_____________________________________________
  Let us list the factors of "-22" :
____________________________________________
-2, 11;  </span>→ -2 + 11 = 9 ;<span>
-11, 2;  </span>→ -11 + 2 = -9 ;<span>
____________________________________________

So we have:  "-2" and "11" ;
____________________________________________
So;   </span>  "x² + 9x − 22" ; factors into " (x−2)(x + 11)" ;
____________________________________________
We have:  (x−2)(x + 11) = 0 ;

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   x + 11 = 0 ;

Subtract "11" from each side of the equation;

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      x = -11 ; 
___________________________________
 Answer:  x = 2 ; -11 .
___________________________________
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