Express z_(1)=3[cos(60^(@))+i sin(60^(@))]" in " rectangular form. Express your answer in exact terms. z_(1)=◻+=^(+x)

Identify trigonometric form: Identify the trigonometric form of the complex number. The given complex number is in trigonometric form: z_1 = 3[cos(60°) + i sin(60°)]. To convert it to rectangular form, we need to evaluate the cosine and sine functions.Evaluate cosine and sine: Evaluate the cosine and sine of 60 degrees. Cosine and sine of 60 degrees are known values: cos(60°) = 1/2 sin(60°) = √3/2Substitute values into trigonometric form: Substitute the values of cosine and sine into the trigonometric form. z_1 = 3[(1/2) + i(√3/2)]Distribute coefficient: Distribute the coefficient 3 to both the real and imaginary parts. z_1 = 3 * (1/2) + 3 * i(√3/2) z_1 = (3/2) + (3√3/2)iWrite final answer in rectangular form: Write the final answer in rectangular form. The rectangular form of the complex number is z_1 = (3/2) + (3√3/2)i.

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Express

z_(1)=3[cos(60^(@))+i sin(60^(@))]" in "
rectangular form.
Express your answer in exact terms.

z_(1)=◻+=^(+x)

Express $z_{1}=3\left[\cos \left(60^{\circ}\right)+i \sin \left(60^{\circ}\right)\right] \text { in }$ rectangular form. $\newline$ Express your answer in exact terms. $\newline$ $z_{1}=\square$

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Algebra 1

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Q. Express

z_{1}=3\left[\cos \left(60^{\circ}\right)+i \sin \left(60^{\circ}\right)\right] \text { in }

rectangular form.

\newline

Express your answer in exact terms.

\newline

z_{1}=\square

Identify trigonometric form: Identify the trigonometric form of the complex number. $\newline$ The given complex number is in trigonometric form: $z_1 = 3[\cos(60°) + i \sin(60°)]$ . To convert it to rectangular form, we need to evaluate the cosine and sine functions.
Evaluate cosine and sine: Evaluate the cosine and sine of $60$ degrees. $\newline$ Cosine and sine of $60$ degrees are known values: $\newline$ $\cos(60^\circ) = \frac{1}{2}$ $\newline$ $\sin(60^\circ) = \frac{\sqrt{3}}{2}$
Substitute values into trigonometric form: Substitute the values of cosine and sine into the trigonometric form. $z_1 = 3\left[\frac{1}{2} + i\left(\frac{\sqrt{3}}{2}\right)\right]$
Distribute coefficient: Distribute the coefficient $3$ to both the real and imaginary parts. $\newline$ $z_1 = 3 \times (\frac{1}{2}) + 3 \times i(\frac{\sqrt{3}}{2})$ $\newline$ $z_1 = (\frac{3}{2}) + (\frac{3\sqrt{3}}{2})i$
Write final answer in rectangular form: Write the final answer in rectangular form. $\newline$ The rectangular form of the complex number is $z_1 = \frac{3}{2} + \frac{3\sqrt{3}}{2}i$ .