How do you write the trigonometric form into a complex number in standard form $4 (cos 135 + i sin 135)$ $4(cos135+isin135)$ ?

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How do you write the trigonometric form into a complex number in standard form $4 (cos 135 + i sin 135)$ $4(cos135+isin135)$ ?

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Answer 1 · 2016-09-10T14:53:34

$4 ({cos 135}^{o} + i {sin 135}^{o}) = - 2 \sqrt{2} + 2 i \sqrt{2}$ $4(cos135^o + isin135^o)=-2sqrt2+2isqrt2$

Explanation:

As ${cos 135}^{o} = cos (180^{o} - 45^{o}) = - {cos 45}^{o} = - \frac{1}{\sqrt{2}}$ $cos135^o=cos(180^o-45^o)=-cos45^o=-1/sqrt2$ and

${sin 135}^{o} = sin (180^{o} - 45^{o}) = {sin 45}^{o} = \frac{1}{\sqrt{2}}$ $sin135^o=sin(180^o-45^o)=sin45^o=1/sqrt2$

Hence $4 ({cos 135}^{o} + i {sin 135}^{o})$ $4(cos135^o + isin135^o)$

= $4 (- \frac{1}{\sqrt{2}} + i \times \frac{1}{\sqrt{2}})$ $4(-1/sqrt2+ixx1/sqrt2)$

= $- \frac{4}{\sqrt{2}} + 4 \frac{i}{\sqrt{2}}$ $-4/sqrt2+4i/sqrt2$

But as $\frac{4}{\sqrt{2}} = \frac{4}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = 4 \frac{\sqrt{2}}{2} = 2 \sqrt{2}$ $4/sqrt2=4/sqrt2xxsqrt2/sqrt2=4sqrt2/2=2sqrt2$

$4 ({cos 135}^{o} + i {sin 135}^{o}) = - 2 \sqrt{2} + 2 i \sqrt{2}$ $4(cos135^o + isin135^o)=-2sqrt2+2isqrt2$

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How do you write the trigonometric form into a complex number in standard form $4 (cos 135 + i sin 135)$ $4(cos135+isin135)$ ?

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Humanities

... and beyond

How do you write the trigonometric form into a complex number in standard form 4(cos135+isin135)4(cos135+isin135)?

1 Answer

Explanation:

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How do you write the trigonometric form into a complex number in standard form $4 (cos 135 + i sin 135)$ $4(cos135+isin135)$ ?