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Write the complex number in the form a + bi. five divided by two (cos 150° + i sin 150°)

User EscoMaji
by
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2 Answers

4 votes

Answer:

d

Explanation:

edge 2020

User Norbeq
by
7.3k points
4 votes

Answer:

Explanation:

The given complex number is :


(5)/(2)(cos150^(\circ)+isin150^(\circ))

Now, we know that
cos150^(\circ)=cos(90^(\circ)+60^(\circ))=-sin60^(\circ)=-(√(3))/(2) and


sin(150^(\circ))=sin(90^(\circ)+60^(\circ))=cos60^(\circ)=(1)/(2)

Therefore, substituting the values in the given complex number, we get


(5)/(2)((-√(3))/(2)+i((1)/(2)))

=
(5)/(2)((-√(3))/(2)+((i)/(2)))

=
(-5√(3))/(4)+(5i)/(4)

Which is in the form of a+bi where a=
(-5√(3))/(4) and b=
(5)/(4)

User Natros
by
7.7k points