Solve Complex Number Equation - V(o) = 183.53-j14.12

In summary, a complex number equation is an equation that includes numbers with both real and imaginary parts. To solve it, you can use the rules of arithmetic for complex numbers and isolate the variable using algebraic properties. The value of V(o) in a given complex number equation is represented by a complex number with a real part of 183.53 and an imaginary part of -14.12. Complex numbers can also be represented in polar form by converting from rectangular form and can be graphed on a Cartesian plane. The horizontal axis represents the real part and the vertical axis represents the imaginary part, with the origin at (0 + 0i).
  • #1
stau40
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Homework Statement


I'm working on a circuits equation and need to find V(o). The equation is: (V(o)/-j25)+((V(o)-240)/12.5)+(V(o)/(15+j20))=0 How do I solve for V(o)? I know the answer is 183.53-j14.12, but I don't understand how to get to that answer. Thanks in advance!


Homework Equations





The Attempt at a Solution


 
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  • #2
1st step: multiply by -j25 * 12.5 * (15+j20)
 

Related to Solve Complex Number Equation - V(o) = 183.53-j14.12

1. What is a complex number equation?

A complex number equation is an equation that contains complex numbers, which are numbers that have both a real part and an imaginary part. These numbers are represented in the form a + bi, where a is the real part and bi is the imaginary part (with i being the imaginary unit).

2. How do you solve a complex number equation?

To solve a complex number equation, you can use the rules of arithmetic for complex numbers. First, you can combine like terms and then use the distributive property to simplify the equation. Next, you can isolate the variable by adding or subtracting the same quantity from both sides of the equation. Finally, you can solve for the variable using the properties of complex numbers.

3. What is the value of V(o) in the given complex number equation?

The value of V(o) is 183.53-j14.12. This represents a complex number with a real part of 183.53 and an imaginary part of -14.12.

4. How can I represent a complex number in polar form?

A complex number can be represented in polar form by converting it from rectangular form (a + bi) to polar form (r(cosθ + isinθ)). To do this, you can use the Pythagorean theorem to find the magnitude (r) and use trigonometric functions to find the angle (θ).

5. Can complex numbers be graphed on a Cartesian plane?

Yes, complex numbers can be graphed on a Cartesian plane. The horizontal axis represents the real part of the complex number (a) and the vertical axis represents the imaginary part (bi). The point where these two axes intersect represents the origin (0 + 0i). The magnitude and angle of the complex number can also be represented on this graph.

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