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Sagot :
The required polar form of the equation is [tex]Z = 5/2cos30 - 5/2sin30i.[/tex]
For the complex number z = (5sqrt(3))/4 - 5/4 * i the polar form is to be determined.
What is a complex number?
The number that constitutes real and imaginary numbers are called complex numbers. The standard form of complex number = a + bi
[tex]z = 5\sqrt{3}/4 - 5/4i[/tex]
the polar form complex numbner can be given as
[tex]z = rcos\theta +rsin\theta i[/tex] - - - - - -(1)
where r = [tex]\sqrt{a^2+b^2}[/tex]
and [tex]\theta=tan^-\frac{b}{a}[/tex]
Since a = 5√3/4 and b = -5/4
[tex]r = \sqrt{(5\sqrt{3}/4)^2+(5/4)^2}[/tex]
r = 10/4
r = 5/2
Now,
[tex]\theta=tan^-\frac{b}{a}[/tex]
[tex]\theta=tan^-\frac{-5/4}{5\sqrt{3}/4 }\\\theta=tan^-\frac{1}{\sqrt{3} }\\\theta=tan^-(-tan30)\\\theta=-30[/tex]
Now the polar form is given by substituting the values of r and [tex]\theta[/tex] in equation 1
Here,
[tex]z = 5/2cos30 +5/2sin(-30)i\\z = 5/2cos30-5/2sin30 i[/tex]
Thus, the required polar form of the equation is [tex]Z = 5/2cos30 - 5/2sin30i.[/tex]
Learn more about complex numbers here: https://brainly.com/question/28007020
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