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Find the current that will flow when $V=1.6-0.3 i$ volts and $Z=1.5+8 i$ ohms using theformula $Z=\frac{V}{I} .$

$-0 \cdot 2 i$

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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are in this problem were given home saw which sites that Z equals V over on where eyes the current. And that is the variable we are hoping to solve for. And also we're given that Z equals 1.5 plus eight. And that V equals 1.6. Monastery 0.3. So moving right along to step number three. Um, after rearranging the equation, we have that out of the current, which we're hoping to solve for is equal to 1.6 Monastery three I divided by 1.5 plus eight. Now we're going to need to multiply both the numerator and the denominator of this fraction by the complex conjure git of the denominator. Okay. And that is actually 1.5 minus eight up. So we will need to foil both the numerator and denominator. Moving on to step for these calculations have been performed. Um, 1.6 times. 1.5 is 2.4 on our outer terms. Multiply. They're going to give us monastery 0.8, uh, and moving right along, Uh, and the same processes follow for the denominator, which is shown. Okay, so we have an odd squared in both the numerator and denominator. So that is going to make, um, this plus 2.4 square into modest into modest 2.4. Because ah, square, discourage of negative one squared, which will turn the plus 2.42 minus 2.4. And lock wasn't the denominator. We have negative 64 r squared, which is negative. 64 times negative. One amount of 64 in the plus 64. So now we have our current is equal to 2.4 modest 2.4 and the nominators. That leaves us a really component of zero. Now we have negative 12.8, and then we have the monitors of the 0.45 Um, okay, And that is going to leave us with, um mon ist 13.25 And that is going to be our imaginary component for the numerator. Now, in the denominator, we have a plus. Drove on a monastery, ola, and they're going to cancel out. And then we have a plus 2.25 plus 64 which is 66.25 Now. Our final answer is therefore negative 13.25 divided by 66.25 I we can simplify this further using a calculator, and we will rob a final answer of negative 0.2 ah as our current or very.

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