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Impedance is the resistance to the flow of current in an electric circuit measured in ohms.The impedance, $Z,$ in a circuit is found by using the formula $Z=\frac{V}{I}$ where $V$ is the voltage(measured in volts) and $I$ is the current (measured in amperes). Find the impedance when$V=1.8-0.4 i$ volts and $I=-0.3 i$ amperes.

$i^{2}=-1$

Algebra

Chapter 5

QUADRATIC FUNCTIONS AND COMPLEX NUMBERS

Section 5

Operations with Complex Numbers

Equations and Inequalities

Quadratic Functions

Complex Numbers

Polynomials

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All right. So here we have an application of complex numbers. We have the electric circuit. Z is impedance these voltage eyes current, and we were given some numbers for voltage and current and were asked to find the impedance. So let's go ahead and substitute those into the equation. And we have 1.8 minus 0.4 i over negative 0.3 I. Now let's go ahead and change that to standard form so we should multiply the numerator and denominator by I that'll do it. Weaken, weaken multiplied by more later if we need to. So that ends up giving us 1.8 I minus 0.4. I squared over negative 0.3 times I squared and everywhere we see I squared, we can replace it with negative one. So we have 1.8 I minus 0.4 times negative, one over negative, 0.3 times negative one. Let's simplify that a little bit more and we have 1.8 I plus 0.4 divided by 0.3. And to finish this off writing it in standard form, the rial part would be 0.4 divided by 0.3 and that simplifies to be 4/3. And then the imaginary part is going to be 1.8. I divided by 0.31 point eight divided by 80.3 is six. So that's going to be six I. So we get 4/3 plus six I

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