Find magnitude: \(|a+bi|=\sqrt{{a}^{2}+{b}^{2}}\).
\[\sqrt{{z}^{2}+{3}^{2}}\]
Simplify \(|z+3\imath |\) to \(\sqrt{{z}^{2}+{3}^{2}}\).
\[\sqrt{{z}^{2}+{3}^{2}}-overl\imath nez=1+2\]
Simplify \({3}^{2}\) to \(9\).
\[\sqrt{{z}^{2}+9}-overl\imath nez=1+2\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[\sqrt{{z}^{2}+9}-ov{e}^{2}rl\imath nz=1+2\]
Regroup terms.
\[\sqrt{{z}^{2}+9}-{e}^{2}\imath ovrlnz=1+2\]
Simplify \(1+2\) to \(3\).
\[\sqrt{{z}^{2}+9}-{e}^{2}\imath ovrlnz=3\]
Subtract \(\sqrt{{z}^{2}+9}\) from both sides.
\[-{e}^{2}\imath ovrlnz=3-\sqrt{{z}^{2}+9}\]
Divide both sides by \(-{e}^{2}\).
\[\imath ovrlnz=-\frac{3-\sqrt{{z}^{2}+9}}{{e}^{2}}\]
Divide both sides by \(\imath \).
\[ovrlnz=-\frac{\frac{3-\sqrt{{z}^{2}+9}}{{e}^{2}}}{\imath }\]
Simplify \(\frac{\frac{3-\sqrt{{z}^{2}+9}}{{e}^{2}}}{\imath }\) to \(\frac{3-\sqrt{{z}^{2}+9}}{{e}^{2}\imath }\).
\[ovrlnz=-\frac{3-\sqrt{{z}^{2}+9}}{{e}^{2}\imath }\]
Divide both sides by \(v\).
\[orlnz=-\frac{\frac{3-\sqrt{{z}^{2}+9}}{{e}^{2}\imath }}{v}\]
Simplify \(\frac{\frac{3-\sqrt{{z}^{2}+9}}{{e}^{2}\imath }}{v}\) to \(\frac{3-\sqrt{{z}^{2}+9}}{{e}^{2}\imath v}\).
\[orlnz=-\frac{3-\sqrt{{z}^{2}+9}}{{e}^{2}\imath v}\]
Divide both sides by \(r\).
\[olnz=-\frac{\frac{3-\sqrt{{z}^{2}+9}}{{e}^{2}\imath v}}{r}\]
Simplify \(\frac{\frac{3-\sqrt{{z}^{2}+9}}{{e}^{2}\imath v}}{r}\) to \(\frac{3-\sqrt{{z}^{2}+9}}{{e}^{2}\imath vr}\).
\[olnz=-\frac{3-\sqrt{{z}^{2}+9}}{{e}^{2}\imath vr}\]
Divide both sides by \(l\).
\[onz=-\frac{\frac{3-\sqrt{{z}^{2}+9}}{{e}^{2}\imath vr}}{l}\]
Simplify \(\frac{\frac{3-\sqrt{{z}^{2}+9}}{{e}^{2}\imath vr}}{l}\) to \(\frac{3-\sqrt{{z}^{2}+9}}{{e}^{2}\imath vrl}\).
\[onz=-\frac{3-\sqrt{{z}^{2}+9}}{{e}^{2}\imath vrl}\]
Divide both sides by \(n\).
\[oz=-\frac{\frac{3-\sqrt{{z}^{2}+9}}{{e}^{2}\imath vrl}}{n}\]
Simplify \(\frac{\frac{3-\sqrt{{z}^{2}+9}}{{e}^{2}\imath vrl}}{n}\) to \(\frac{3-\sqrt{{z}^{2}+9}}{{e}^{2}\imath vrln}\).
\[oz=-\frac{3-\sqrt{{z}^{2}+9}}{{e}^{2}\imath vrln}\]
Divide both sides by \(z\).
\[o=-\frac{\frac{3-\sqrt{{z}^{2}+9}}{{e}^{2}\imath vrln}}{z}\]
Simplify \(\frac{\frac{3-\sqrt{{z}^{2}+9}}{{e}^{2}\imath vrln}}{z}\) to \(\frac{3-\sqrt{{z}^{2}+9}}{{e}^{2}\imath vrlnz}\).
\[o=-\frac{3-\sqrt{{z}^{2}+9}}{{e}^{2}\imath vrlnz}\]
o=-(3-sqrt(z^2+9))/(e^2*IM*v*r*l*n*z)
