A complex number z_(1) has a magnitude |z_(1)|=18 and an angle theta_(1)=122^(@). 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 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.Calculate Real Part: First, calculate the real part a: a = 18 * cos(122 degrees). Using a calculator, we find a ≈ 18 * (-0.5299) ≈ -9.5382.Calculate Imaginary Part: Now, calculate the imaginary part b: b = 18 * sin(122 degrees). Using a calculator, we find b ≈ 18 * 0.8480 ≈ 15.264.Round to Nearest Thousandth: Round a and b to the nearest thousandth. a ≈ -9.538 and b ≈ 15.264.

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A complex number
z_(1) has a magnitude
|z_(1)|=18 and an angle
theta_(1)=122^(@).
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 $\left|z_{1}\right|=18$ and an angle $\theta_{1}=122^{\circ}$ . $\newline$ 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|=18

and an angle

\theta_{1}=122^{\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 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.
Calculate Real Part: First, calculate the real part $a$ : $a = 18 \times \cos(122^\circ)$ . Using a calculator, we find $a \approx 18 \times (-0.5299) \approx -9.5382$ .
Calculate Imaginary Part: Now, calculate the imaginary part $b$ : $b = 18 \times \sin(122^\circ)$ . Using a calculator, we find $b \approx 18 \times 0.8480 \approx 15.264$ .
Round to Nearest Thousandth: Round $a$ and $b$ to the nearest thousandth. $a \approx -9.538$ and $b \approx 15.264$ .