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valentina_108 [34]

3 years ago

9

Simplify the expression (-2+4i)-(2+7i) I am not great at these--

2 answers:

e-lub [12.9K]3 years ago

8 0

$( - 2 + 4i) - (2 + 7i) \\ ( - 2 + 4i) + ( - 2 - 7i) \\ - 2 + ( - 2) = - 4 \\ 4i + ( - 7i) = - 3i \\ - 4 - 3i$

Gre4nikov [31]3 years ago

3 0

(-2+4i)-(2+7i)
-2+4i+(-2-7i)
Remove ( )
-2+4i+-2-7i
-4+4i-7i
-4-3i Is the answer. Nope this helps.

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Tcecarenko [31]

$\bold{\huge{\green{\underline{ Solution}}}}$

$\bold{\underline{ Given :- }}$

<u>We </u><u>have </u><u>given </u><u>a</u><u> </u><u>right</u><u> </u><u>angled </u><u>triangle </u><u>whose </u><u>values </u><u>are </u><u>m</u><u>, </u><u> </u><u>n </u><u>and </u><u>2</u><u> </u>

$\bold{\underline{ To \: Find :- }}$

<u>We </u><u>have </u><u>to </u><u>find </u><u>the </u><u>value </u><u>of </u><u>m </u><u>and </u><u>n</u>

$\bold{\underline{ Let's \: Begin :- }}$

<u>In </u><u>the </u><u>given </u><u>right </u><u>angled </u><u>triangle</u><u>, </u><u>we </u><u>have </u>

Perpendicular height = n units
Base = 2 units
Hypotenuse = m units

<u>Now</u><u>, </u><u> </u><u>By </u><u>using </u><u>trigonometric </u><u>ratios </u>

$\bold{\pink{ Sin Φ = }}{\bold{\pink{\frac{Perpendicular }{Hypotenuse}}}}$

$\bold{\red{ Cos Φ = }}{\bold{\red{\frac{Base}{Hypotenuse }}}}$

$\bold{\blue { tan Φ = }}{\bold{\blue{\frac{Perpendicular }{Base }}}}$

<u>According </u><u>to </u><u>the </u><u>question </u><u>:</u><u>-</u>

$\bold{ Cos \: 45° = }{\bold{\frac{2}{m}}}$

$\bold{ 1/√2= }{\bold{\frac{2}{m}}}$

$\bold{\red{ m = 2√2 \: units }}$

<u>We </u><u>know </u><u>that </u><u>,</u><u> </u><u>Sum </u><u>of </u><u>Angles</u><u> </u><u>of </u><u>triangle </u><u>is </u><u>1</u><u>8</u><u>0</u><u>°</u><u> </u><u>.</u>

<u>Therefore</u><u>, </u>

Let the unknown angle be x

$\sf{ 45° + x + 90° = 180° }$

$\sf{ x = 180° - 135 ° }$

$\sf{ x = 45° }$

<u>Now</u><u>, </u>

$\bold{ Cos \: x° = }{\bold{\frac{n}{2√2}}}$

$\bold{ Cos \: 45° = }{\bold{\frac{n}{2√2}}}$

$\bold{ 1/√2= }{\bold{\frac{n}{2√2}}}$

$\bold { n = 2√2/√2 }$

$\bold{\red{ n = 2\: units }}$

Thus, The value of m = 2√2 and n = 2

$\sf{\blue{ Hence, \: option \: D \: is \: Correct }}$

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