Question

express the following in polar form 5÷2(cos300°+isin30°)​

Answer 1

Answer:

The standard form of the given complex number is $\frac{5}{4}-i\frac{5\sqrt3}{4}$

Step-by-step explanation:

Express the following in standard form

$\frac{5}{2}(cos300+isin300)$

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concept used:

The standaard form of a complex number is z=x+iy

Now,

$\frac{5}{2}(cos300+isin300)$

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$=\frac{5}{2}[cos300+isin300]$

$=\frac{5}{2}[cos(270+30)+isin(270+30)]$

$=\frac{5}{2}[sin30-icos30]$

$=\frac{5}{2}[\frac{1}{2}-i\frac{\sqrt3}{2}]$

$=\frac{5}{2}*\frac{1}{2}-i\frac{5}{2}*\frac{\sqrt3}{2}$

$=\frac{5}{4}-i\frac{5\sqrt3}{4}$