How do you write the trigonometric form in complex form $\frac{3}{4} (cos (\frac{7 π}{4}) + i sin (\frac{7 π}{4})))$ $3/4(cos((7pi)/4)+isin((7pi)/4)))$ ?

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How do you write the trigonometric form in complex form $\frac{3}{4} (cos (\frac{7 π}{4}) + i sin (\frac{7 π}{4})))$ $3/4(cos((7pi)/4)+isin((7pi)/4)))$ ?

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Answer 1 · 2016-08-10T13:42:26

$z = \frac{3 \sqrt{2}}{8} - \frac{3 \sqrt{2}}{8} i$ $z=(3sqrt2)/8-(3sqrt2)/8 i$

Explanation:

Starting with the trig. part

That is $cos (\frac{7 π}{4}) + i sin (\frac{7 π}{4})$ $cos((7pi)/4)+isin((7pi)/4)$

Simplifying this as follows.

$Reminder$ $color(orange)"Reminder"$

$color(red)(|bar(ul(color(white)(a/a)color(black)(cos((7pi)/4)=cos(2pi-(7pi)/4)=cos(pi/4)color(white)(a/a)|$

and $color(red)(|bar(ul(color(white)(a/a)color(black)(sin((7pi)/4)=-sin(2pi-(7pi)/4)=-sin(pi/4)color(white)(a/a)|)))$

$rArrcos((7pi)/4)+isin((7pi)/4)=cos(pi/4)-isin(pi/4)$

$color(orange)"Reminder" color(red)(|bar(ul(color(white)(a/a)color(black)(cos(pi/4)=sin(pi/4)=1/(sqrt2))color(white)(a/a)|)))$

$rArrcos(pi/4)-isin(pi/4)=1/sqrt2-1/sqrt2 i=sqrt2/2-sqrt2/2 i$

Finally the whole expression becomes.

$3/4(sqrt2/2-sqrt2/2 i)=(3sqrt2)/8-(3sqrt2)/8 i" in complex form"$

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How do you write the trigonometric form in complex form $\frac{3}{4} (cos (\frac{7 π}{4}) + i sin (\frac{7 π}{4})))$ $3/4(cos((7pi)/4)+isin((7pi)/4)))$ ?

1 Answer

Explanation:

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How do you write the trigonometric form in complex form 3/4(cos((7pi)/4)+isin((7pi)/4)))34(cos(7π4)+isin(7π4)))3/4(cos((7pi)/4)+isin((7pi)/4)))?

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Explanation:

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How do you write the trigonometric form in complex form $\frac{3}{4} (cos (\frac{7 π}{4}) + i sin (\frac{7 π}{4})))$ $3/4(cos((7pi)/4)+isin((7pi)/4)))$ ?