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Algebra II

Find the value of x such that -12x=18.

Marissa Singh 2022-05-17

Find the value of m such that 20m=18.

garcialdaria2zky1 2022-05-17

Find the value of y such that 4y=19.

quorums15lep 2022-05-17

Calculate the value of s such that -11s equals 17.

fetsBedscurce4why1 2022-05-17

Calculate the value of x such that 19x equals 18.

oglasnak9h01 2022-05-17

Calculate $(\frac{5}{4} + 7 i) - (4 + \frac{3 i}{8})$ .

othereyeshmt4l 2022-05-17

Simplify: $(5 + 12 i) - (\frac{2}{3} + \frac{7 i}{5})$ .

Aedan Gonzales 2022-05-17

Calculate $(4 + 15 i) - (\frac{4}{3} + \frac{9 i}{8})$ .

measgachyx5q9 2022-05-17

Calculate $(7 + 10 i) - (\frac{4}{7} + \frac{i}{3})$ .

sg101cp6vv 2022-05-17

Calculate $(\frac{7}{18} + 3 i) - (5 + \frac{2 i}{7})$ .

Jay Barrett 2022-05-17

Compute $(14 + \frac{i}{3}) - (\frac{18}{5} + 6 i)$ .

et1wdwk4o 2022-05-17

Add 4+3i and $\frac{6}{7} + \frac{2 i}{3}$ .

Azzalictpdv 2022-05-17

Add 3+5i and $\frac{5}{6} + \frac{3 i}{4}$ .

Stoyanovahvsbh 2022-05-17

Calculate $(\frac{3}{4} + \frac{17 i}{18}) + (7 + 15 i)$ .

Eve Dunn 2022-05-17

Add $\frac{5}{12} + 4 i$ and $11 + \frac{7 i}{6}$ .

London Ware 2022-05-17

Add $\frac{3}{8} + \frac{14 i}{11}$ and 3+8i.

Alaina Holt 2022-05-17

This is from the page 19 of the book called An Introduction to Complex Function Theory by Bruce P. Palka.
Every rational function of z=x+iy is clearly a rational function of x and y, but not the other way around.
As a reminder, a rational function of z=x+iy is defined as $f (z) = \frac{a_{0} + a_{1} z + \dots + a_{n} z^{n}}{b_{0} + b_{1} z + \dots b_{m} z^{m}}$ . I understand the first part of the claim: if z is fixed, i.e. both x and y are fixed, then of course all combinations of as and bs are part of the set where as, bs, xs and ys can vary. But I don't see why this wouldn't hold the other way around. Specifically, why cannot we choose the coefficients $a_{0}, \dots, a_{n}$ and $b_{0}, \dots, b_{m}$ in such a way that any change in x or y is mitigated?

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Algebra II