A complex number z_(1) has a magnitude |z_(1)|=9 and an angle theta_(1)=50^(@). Express z_(1) in rectangular form, as z_(1)=a+bi. Round a and b to the nearest thousandth. z_(1)=◻+◻i

Formulas Used: To convert a complex number from polar to rectangular form, we use the formulas a = r * cos(theta) and b = r * sin(theta), where r is the magnitude and theta is the angle in degrees.Calculate Real Part: First, we calculate the real part a of the complex number z_(1). We have r = 9 and theta = 50 degrees. So, a = 9 * cos(50 degrees).Calculate Imaginary Part: Using a calculator, we find that cos(50 degrees) ≈ 0.64279. Therefore, a = 9 * 0.64279.Calculating the value of a gives us a ≈ 9 * 0.64279 ≈ 5.78511. We round this to the nearest thousandth, which gives us a ≈ 5.785.Next, we calculate the imaginary part b of the complex number z_(1). We have r = 9 and theta = 50 degrees. So, b = 9 * sin(50 degrees).Using a calculator, we find that sin(50 degrees) ≈ 0.76604. Therefore, b = 9 * 0.76604.Calculating the value of b gives us b ≈ 9 * 0.76604 ≈ 6.89436. We round this to the nearest thousandth, which gives us b ≈ 6.894.

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A complex number
z_(1) has a magnitude
|z_(1)|=9 and an angle
theta_(1)=50^(@).
Express
z_(1) in rectangular form, as
z_(1)=a+bi.
Round
a and
b to the nearest thousandth.

z_(1)=◻+◻i

A complex number $z_{1}$ has a magnitude $\left|z_{1}\right|=9$ and an angle $\theta_{1}=50^{\circ}$ . $\newline$ Express $z_{1}$ in rectangular form, as $z_{1}=a+b i$ . $\newline$ Round $a$ and $b$ to the nearest thousandth. $\newline$ $z_{1}=\square+\square i$

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Q. A complex number

z_{1}

has a magnitude

\left|z_{1}\right|=9

and an angle

\theta_{1}=50^{\circ}

\newline

Express

z_{1}

in rectangular form, as

z_{1}=a+b i

\newline

Round

a

and

b

to the nearest thousandth.

\newline

z_{1}=\square+\square i

Formulas Used: To convert a complex number from polar to rectangular form, we use the formulas $a = r \cdot \cos(\theta)$ and $b = r \cdot \sin(\theta)$ , where $r$ is the magnitude and $\theta$ is the angle in degrees.
Calculate Real Part: First, we calculate the real part $a$ of the complex number $z_{1}$ . We have $r = 9$ and $\theta = 50$ degrees. So, $a = 9 \times \cos(50 \text{ degrees})$ .
Calculate Imaginary Part: Using a calculator, we find that $\cos(50^\circ) \approx 0.64279$ . Therefore, $a = 9 \times 0.64279$ .
Calculate Imaginary Part: Using a calculator, we find that $\cos(50^\circ) \approx 0.64279$ . Therefore, $a = 9 \times 0.64279$ .Calculating the value of $a$ gives us $a \approx 9 \times 0.64279 \approx 5.78511$ . We round this to the nearest thousandth, which gives us $a \approx 5.785$ .
Calculate Imaginary Part: Using a calculator, we find that $\cos(50^\circ) \approx 0.64279$ . Therefore, $a = 9 \times 0.64279$ . Calculating the value of $a$ gives us $a \approx 9 \times 0.64279 \approx 5.78511$ . We round this to the nearest thousandth, which gives us $a \approx 5.785$ . Next, we calculate the imaginary part $b$ of the complex number $z_{1}$ . We have $r = 9$ and $\theta = 50^\circ$ . So, $b = 9 \times \sin(50^\circ)$ .
Calculate Imaginary Part: Using a calculator, we find that $\cos(50^\circ) \approx 0.64279$ . Therefore, $a = 9 \times 0.64279$ . Calculating the value of $a$ gives us $a \approx 9 \times 0.64279 \approx 5.78511$ . We round this to the nearest thousandth, which gives us $a \approx 5.785$ . Next, we calculate the imaginary part $b$ of the complex number $z_{1}$ . We have $r = 9$ and $\theta = 50^\circ$ . So, $b = 9 \times \sin(50^\circ)$ . Using a calculator, we find that $a = 9 \times 0.64279$ $0$ . Therefore, $a = 9 \times 0.64279$ $1$ .
Calculate Imaginary Part: Using a calculator, we find that $\cos(50^\circ) \approx 0.64279$ . Therefore, $a = 9 \times 0.64279$ . Calculating the value of $a$ gives us $a \approx 9 \times 0.64279 \approx 5.78511$ . We round this to the nearest thousandth, which gives us $a \approx 5.785$ . Next, we calculate the imaginary part $b$ of the complex number $z_{1}$ . We have $r = 9$ and $\theta = 50^\circ$ . So, $b = 9 \times \sin(50^\circ)$ . Using a calculator, we find that $a = 9 \times 0.64279$ $0$ . Therefore, $a = 9 \times 0.64279$ $1$ . Calculating the value of $b$ gives us $a = 9 \times 0.64279$ $3$ . We round this to the nearest thousandth, which gives us $a = 9 \times 0.64279$ $4$ .