What is the trigonometric form of $(2 - 4 i) \cdot (3 - 2 i)$ $(2-4i)*(3-2i)$ ?

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What is the trigonometric form of $(2 - 4 i) \cdot (3 - 2 i)$ $(2-4i)*(3-2i)$ ?

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Answer 1 · 2017-07-03T17:07:34

See the explanation below.

Explanation:

First, expand the expression.

$(2 - 4 i) \cdot (3 - 2 i)$ $(2-4i) * (3-2i)$
= $6 - 4 i - 12 i + 8 i^{2}$ $6 - 4i - 12i +8i^2$
= $6 - 4 i - 12 i - 8$ $6 - 4i - 12i -8$
= $- 2 - 16 i$ $-2 - 16i$

To convert this to trigonometric form, you need to know the values of $r$ $r$ and $θ$ $theta$ .

You can use the following equations:
$r^{2} = x^{2} + y^{2}$ $r^2 = x^2+y^2$ and $tan θ = \frac{y}{x}$ $tan theta = (y)/(x)$

$r^{2} = x^{2} + y^{2}$ $r^2 = x^2+y^2$
$r = \sqrt{x^{2} + y^{2}}$ $r = sqrt(x^2+y^2)$
$r = \sqrt{{(- 2)}^{2} + {(- 16)}^{2}}$ $r = sqrt((-2)^2+(-16)^2)$
$r = 2 \sqrt{65}$ $r = 2sqrt65$

$tan θ = \frac{y}{x}$ $tan theta = (y)/(x)$
$tan θ = \frac{- 16}{- 2}$ $tan theta = (-16)/(-2)$
$tan θ = 8$ $tan theta = 8$
$θ = {tan}^{- 1} (8)$ $theta = tan^-1(8)$
$θ \approx 1.45$ $theta ~~ 1.45$

So, the answer is $2 \sqrt{65}$ $2sqrt65$ $c i s$ $cis$ $1.45$ $1.45$ or $2 \sqrt{65} (cos 1.45 + i sin 1.45)$ $2sqrt65 (cos 1.45 + i sin 1.45)$ .

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What is the trigonometric form of $(2 - 4 i) \cdot (3 - 2 i)$ $(2-4i)*(3-2i)$ ?

1 Answer

Explanation:

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What is the trigonometric form of (2−4i)⋅(3−2i) (2-4i)*(3-2i) ?

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What is the trigonometric form of $(2 - 4 i) \cdot (3 - 2 i)$ $(2-4i)*(3-2i)$ ?