Express Complex Numbers In Rectangular Form - Pre-Calculus

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Convert $5(\cos $\frac{ 8 \pi }{5}$ + i \sin $\frac{ 8 \pi }{5}$ )$ to rectangular form

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To convert, evaluate the trig ratios and then distribute the radius:

Convert the following to rectangular form:

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Distribute the coefficient and simplify:

$\ 3(cos(60)-isin(30))\ \=3sin(60)-i(3sin(30)))\ \=\frac{3}{2}$-$\frac{3}{2}$i$

Convert $6(\cos $\frac{\pi}{5}$ + i \sin $\frac{ \pi }{5}$ )$ in rectangular form

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To convert, just evaluate the trig ratios and then distribute the radius.

Convert $3(\cos $200^o$ + i \sin $200^o$ )$ to rectangular form

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To convert to rectangular form, just evaluate the trig functions and then distribute the radius:

Represent the polar equation:

$z = 3\left(cos($\frac{\pi}{6}$ )+i\cdot sin\left($\frac{\pi}{6}\right)\right)$

in rectangular form.

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Using the general form of a polar equation:

$z = r(cos(\theta) + i\cdot sin(\theta))$

we find that the value of is and the value of $\theta$ is $\frac{\pi}{6}$ .

The rectangular form of the equation appears as , and can be found by finding the trigonometric values of the cosine and sine equations.

$cos\left($\frac{\pi}{6}\right) = $\frac{\sqrt{3}$}{2}$

$sin\left($\frac{\pi}{6}\right) = $\frac{1}{2}$$

distributing the 3, we obtain the final answer of:

$$\frac{3\sqrt{3}$}{2} + $\frac{3}{2}$i$

Represent the polar equation:

$z = 4\left(cos\left($\frac{\pi}{4}\right) + i\cdot sin\left($\frac{\pi}{4}\right)\right)$

in rectangular form.

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Using the general form of a polar equation:

$z = r(cos(\theta) + i\cdot sin(\theta))$

we find that the value of and the value of $\theta =\frac{\pi}{4}$$ . The rectangular form of the equation appears as , and can be found by finding the trigonometric values of the cosine and sine equations.

$cos\left($\frac{\pi}{4}\right) = $\frac{1}{\sqrt{2}$}$

$sin\left($\frac{\pi}{4}\right) = $\frac{1}{\sqrt2}$$

Distributing the 4, we obtain the final answer of:

$z = 2$\sqrt{2}$ + 2$\sqrt{2}$i$

Represent the polar equation:

$z = 5\left(cos\left($\frac{3\pi}{4}\right)+i \cdot sin\left($\frac{3\pi}{4}\right)\right)$

in rectangular form.

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Using the general form of a polar equation:

$z = r(cos(\theta) + i*sin(\theta))$

we find that the value of and the value of $\theta =\frac{3\pi}{4}$$ . The rectangular form of the equation appears as , and can be found by finding the trigonometric values of the cosine and sine equations.

$cos\left($\frac{3\pi}{4}\right) = $\frac{-1}{\sqrt{2}$}$

$sin\left($\frac{3\pi}{4}\right) = $\frac{1}{\sqrt{2}$}$

distributing the 5, we obtain the final answer of:

$$\frac{-5\sqrt{2}$}{2} + $\frac{5\sqrt{2}$}{2}i$

Convert the following to rectangular form:

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Distribute the coefficient 2, and evaluate each term:

$\2(cos(30)+ isin(30))\ \= 2cos(30)+i(2sin(30))\ \=$\sqrt{3}$+i$

Convert $5(\cos $\frac{ 8 \pi }{5}$ + i \sin $\frac{ 8 \pi }{5}$ )$ to rectangular form

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To convert, evaluate the trig ratios and then distribute the radius:

Convert the following to rectangular form:

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Distribute the coefficient and simplify:

$\ 3(cos(60)-isin(30))\ \=3sin(60)-i(3sin(30)))\ \=\frac{3}{2}$-$\frac{3}{2}$i$

Convert $6(\cos $\frac{\pi}{5}$ + i \sin $\frac{ \pi }{5}$ )$ in rectangular form

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To convert, just evaluate the trig ratios and then distribute the radius.

Convert $3(\cos $200^o$ + i \sin $200^o$ )$ to rectangular form

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To convert to rectangular form, just evaluate the trig functions and then distribute the radius:

Represent the polar equation:

$z = 3\left(cos($\frac{\pi}{6}$ )+i\cdot sin\left($\frac{\pi}{6}\right)\right)$

in rectangular form.

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Using the general form of a polar equation:

$z = r(cos(\theta) + i\cdot sin(\theta))$

we find that the value of is and the value of $\theta$ is $\frac{\pi}{6}$ .

The rectangular form of the equation appears as , and can be found by finding the trigonometric values of the cosine and sine equations.

$cos\left($\frac{\pi}{6}\right) = $\frac{\sqrt{3}$}{2}$

$sin\left($\frac{\pi}{6}\right) = $\frac{1}{2}$$

distributing the 3, we obtain the final answer of:

$$\frac{3\sqrt{3}$}{2} + $\frac{3}{2}$i$

Represent the polar equation:

$z = 4\left(cos\left($\frac{\pi}{4}\right) + i\cdot sin\left($\frac{\pi}{4}\right)\right)$

in rectangular form.

Tap to see back →

Using the general form of a polar equation:

$z = r(cos(\theta) + i\cdot sin(\theta))$

we find that the value of and the value of $\theta =\frac{\pi}{4}$$ . The rectangular form of the equation appears as , and can be found by finding the trigonometric values of the cosine and sine equations.

$cos\left($\frac{\pi}{4}\right) = $\frac{1}{\sqrt{2}$}$

$sin\left($\frac{\pi}{4}\right) = $\frac{1}{\sqrt2}$$

Distributing the 4, we obtain the final answer of:

$z = 2$\sqrt{2}$ + 2$\sqrt{2}$i$

Represent the polar equation:

$z = 5\left(cos\left($\frac{3\pi}{4}\right)+i \cdot sin\left($\frac{3\pi}{4}\right)\right)$

in rectangular form.

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Using the general form of a polar equation:

$z = r(cos(\theta) + i*sin(\theta))$

we find that the value of and the value of $\theta =\frac{3\pi}{4}$$ . The rectangular form of the equation appears as , and can be found by finding the trigonometric values of the cosine and sine equations.

$cos\left($\frac{3\pi}{4}\right) = $\frac{-1}{\sqrt{2}$}$

$sin\left($\frac{3\pi}{4}\right) = $\frac{1}{\sqrt{2}$}$

distributing the 5, we obtain the final answer of:

$$\frac{-5\sqrt{2}$}{2} + $\frac{5\sqrt{2}$}{2}i$

Convert the following to rectangular form:

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Distribute the coefficient 2, and evaluate each term:

$\2(cos(30)+ isin(30))\ \= 2cos(30)+i(2sin(30))\ \=$\sqrt{3}$+i$

Represent the polar equation:

$z = 3\left(cos($\frac{\pi}{6}$ )+i\cdot sin\left($\frac{\pi}{6}\right)\right)$

in rectangular form.

Tap to see back →

Using the general form of a polar equation:

$z = r(cos(\theta) + i\cdot sin(\theta))$

we find that the value of is and the value of $\theta$ is $\frac{\pi}{6}$ .

The rectangular form of the equation appears as , and can be found by finding the trigonometric values of the cosine and sine equations.

$cos\left($\frac{\pi}{6}\right) = $\frac{\sqrt{3}$}{2}$

$sin\left($\frac{\pi}{6}\right) = $\frac{1}{2}$$

distributing the 3, we obtain the final answer of:

$$\frac{3\sqrt{3}$}{2} + $\frac{3}{2}$i$

Represent the polar equation:

$z = 4\left(cos\left($\frac{\pi}{4}\right) + i\cdot sin\left($\frac{\pi}{4}\right)\right)$

in rectangular form.

Tap to see back →

Using the general form of a polar equation:

$z = r(cos(\theta) + i\cdot sin(\theta))$

we find that the value of and the value of $\theta =\frac{\pi}{4}$$ . The rectangular form of the equation appears as , and can be found by finding the trigonometric values of the cosine and sine equations.

$cos\left($\frac{\pi}{4}\right) = $\frac{1}{\sqrt{2}$}$

$sin\left($\frac{\pi}{4}\right) = $\frac{1}{\sqrt2}$$

Distributing the 4, we obtain the final answer of:

$z = 2$\sqrt{2}$ + 2$\sqrt{2}$i$

Represent the polar equation:

$z = 5\left(cos\left($\frac{3\pi}{4}\right)+i \cdot sin\left($\frac{3\pi}{4}\right)\right)$

in rectangular form.

Tap to see back →

Using the general form of a polar equation:

$z = r(cos(\theta) + i*sin(\theta))$

we find that the value of and the value of $\theta =\frac{3\pi}{4}$$ . The rectangular form of the equation appears as , and can be found by finding the trigonometric values of the cosine and sine equations.

$cos\left($\frac{3\pi}{4}\right) = $\frac{-1}{\sqrt{2}$}$

$sin\left($\frac{3\pi}{4}\right) = $\frac{1}{\sqrt{2}$}$

distributing the 5, we obtain the final answer of:

$$\frac{-5\sqrt{2}$}{2} + $\frac{5\sqrt{2}$}{2}i$

Convert the following to rectangular form:

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Distribute the coefficient 2, and evaluate each term:

$\2(cos(30)+ isin(30))\ \= 2cos(30)+i(2sin(30))\ \=$\sqrt{3}$+i$