# Write the standard form of the complex number. 12(cos(60^@) + i sin(60^@))

Write the standard form of the complex number.
$12\left(\mathrm{cos}\left({60}^{\circ }\right)+i\mathrm{sin}\left({60}^{\circ }\right)\right)$
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falhiblesw
We know that, ${\mathrm{cos}60}^{\circ }=\frac{1}{2},{\mathrm{sin}60}^{\circ }=\frac{\sqrt{3}}{2}$
Substitute these values in the given complex number,
$z=12\left(\frac{1}{2}+i\frac{\sqrt{3}}{2}$
$z=12\left(\frac{1}{2}\right)+i12\left(\frac{\sqrt{3}}{2}\right)$
$z=6+6\sqrt{3}i$
Therefore,
The standard form of the given complex number is $6+6\sqrt{3}i$
$a=6\phantom{\rule{1em}{0ex}}\text{and}\phantom{\rule{1em}{0ex}}b=6\sqrt{3}$