Express z_(1)=17[cos(pi)+i sin(pi)]" in " rectangular form. Express your answer in exact terms. z_(1)=

Identify Trigonometric Values: To convert a complex number from polar to rectangular form, we use the identities $\cos(\theta)$ and $\sin(\theta)$ to represent the real and imaginary parts, respectively. For $ z_1 = 17[\cos(\pi) + i \sin(\pi)] $, we need to evaluate $\cos(\pi)$ and $\sin(\pi)$.Evaluate Trigonometric Functions: The value of $\cos(\pi)$ is $-1$ and the value of $\sin(\pi)$ is $0$. Therefore, we can substitute these values into the expression for $ z_1 $.Substitute Values: Substituting the values gives us $ z_1 = 17[(-1) + i(0)] $, which simplifies to $ z_1 = 17 \cdot -1 + 17 \cdot 0 \cdot i $.Simplify Expression: Multiplying through, we get $ z_1 = -17 + 0i $, which is the rectangular form of the complex number.

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Express

z_(1)=17[cos(pi)+i sin(pi)]" in "
rectangular form.
Express your answer in exact terms.

z_(1)=

Express $z_{1}=17[\cos (\pi)+i \sin (\pi)] \text { in }$ rectangular form. $\newline$ Express your answer in exact terms. $\newline$ $z_{1}=$

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Algebra 1

Find the inverse of a linear function

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Q. Express

z_{1}=17[\cos (\pi)+i \sin (\pi)] \text { in }

rectangular form.

\newline

Express your answer in exact terms.

\newline

z_{1}=

Identify Trigonometric Values: To convert a complex number from polar to rectangular form, we use the identities $\cos(\theta)$ and $\sin(\theta)$ to represent the real and imaginary parts, respectively. For $z_1 = 17[\cos(\pi) + i \sin(\pi)]$ , we need to evaluate $\cos(\pi)$ and $\sin(\pi)$ .
Evaluate Trigonometric Functions: The value of $\cos(\pi)$ is $-1$ and the value of $\sin(\pi)$ is $0$ . Therefore, we can substitute these values into the expression for $z_1$ .
Substitute Values: Substituting the values gives us $z_1 = 17[(-1) + i(0)]$ , which simplifies to $z_1 = 17 \cdot -1 + 17 \cdot 0 \cdot i$ .
Simplify Expression: Multiplying through, we get $z_1 = -17 + 0i$ , which is the rectangular form of the complex number.