# Write standart form of complex number 5(cos135^@+isin135^@)

Write standart form of complex number $5\left({\mathrm{cos}135}^{\circ }+i{\mathrm{sin}135}^{\circ }\right)$
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Cristiano Sears

Standart form of complex number, $z=r\left(\mathrm{cos}\theta +i\mathrm{sin}\theta \right)$, is z = a+ib
Calculate the values of cosine and sine,
$\mathrm{cos}\left({135}^{\circ }\right)=-\frac{1}{\sqrt{2}}$
$\mathrm{sin}\left({135}^{\circ }=\frac{1}{\sqrt{2}}$
Substitute the values od cosine and sine in $z=5\left({\mathrm{cos}135}^{\circ }+i{\mathrm{sin}135}^{\circ }\right),$
$z=5\left({\mathrm{cos}135}^{\circ }+i{\mathrm{sin}135}^{\circ }\right)=5\left(-\frac{1}{\sqrt{2}}+i\frac{1}{\sqrt{2}}\right)=-\frac{5}{\sqrt{2}}+\frac{t}{\sqrt{2}}i$
Rationalise the complex number, $z=-\frac{5}{\sqrt{2}}+\frac{t}{\sqrt{2}}i,z=-\frac{5\sqrt{2}}{2}+\frac{5\sqrt{2}}{2}i$