Blog: `sqrt(48)[cos(-30^@) + i sin(225^@)]` Write the standard form of the complex number. Then represent the complex number graphically.

Saturday, August 17, 2013

$\displaystyle\sqrt{{{48}}}{\left[{\cos{{\left(-{{30}}^{\circ}\right)}}}+{i}{\sin{{\left({{225}}^{\circ}\right)}}}\right]}$ Write the standard form of the complex number. Then represent the complex number graphically.

Standard form of complex number is were To write the number in standard form we first need to calculate the values of trigonometric functions for the given angle.

$\displaystyle{\cos{{\left(-{{30}}^{\circ}\right)}}}={{\cos{{30}}}}^{\circ}=\frac{\sqrt{{3}}}{{2}}$

$\displaystyle{{\sin{{225}}}}^{\circ}=-{{\sin{{45}}}}^{\circ}=-\frac{\sqrt{{2}}}{{2}}$

We will also write $\displaystyle\sqrt{{48}}$ as $\displaystyle{4}\sqrt{{3}}.$

Therefore, we get

$\displaystyle\sqrt{{48}}{\left({\cos{{\left(-{{30}}^{\circ}\right)}}}+{i}{\sin{{\left({{225}}^{\circ}\right)}}}\right)}=$

$\displaystyle{4}\sqrt{{3}}{\left(\frac{\sqrt{{3}}}{{2}}-\frac{{{i}\sqrt{{2}}}}{{2}}\right)}=$

$\displaystyle{2}\cdot{3}-{2}{i}\sqrt{{6}}=$

$\displaystyle{6}-{2}\sqrt{{6}}{i}$ <--Solution

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Saturday, August 17, 2013

$\displaystyle\sqrt{{{48}}}{\left[{\cos{{\left(-{{30}}^{\circ}\right)}}}+{i}{\sin{{\left({{225}}^{\circ}\right)}}}\right]}$ Write the standard form of the complex number. Then represent the complex number graphically.

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