What is the value of 2(cos((3pi)/4)+isin((3pi)/4)) ?

The value of 2(cos((3pi)/4)+isin((3pi)/4)) is -sqrt(2)+sqrt(2)i

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

2(cos((3pi)/4)+isin((3pi)/4))

2 (cos (\frac{3 π}{4}) + i sin (\frac{3 π}{4}))

- 2 + 2 i

Solution steps

2 (cos (\frac{3 π}{4}) + i sin (\frac{3 π}{4}))

Use the following trivial identity:

cos (\frac{3 π}{4}) = - \frac{2}{2}

cos (\frac{3 π}{4})

cos (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= - \frac{2}{2}

Use the following trivial identity:

sin (\frac{3 π}{4}) = \frac{2}{2}

sin (\frac{3 π}{4})

sin (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{2}{2}

= 2 (- \frac{2}{2} + i \frac{2}{2})

Simplify

2 (- \frac{2}{2} + i \frac{2}{2}) : - 2 + 2 i

2 (- \frac{2}{2} + i \frac{2}{2})

Multiply

i \frac{2}{2} : \frac{2 i}{2}

i \frac{2}{2}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{2 i}{2}

= 2 (- \frac{2}{2} + \frac{2 i}{2})

Simplify

- \frac{2}{2} + \frac{2 i}{2} : \frac{- 2 + 2 i}{2}

- \frac{2}{2} + \frac{2 i}{2}

Apply rule

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{- 2 + 2 i}{2}

= 2 \cdot \frac{- 2 + 2 i}{2}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{( - 2 + 2 i ) \cdot 2}{2}

Cancel the common factor:

2

= - - 2 + 2 i

= - 2 + 2 i

58 sin (5 4^{\circ})

\frac{67}{sin ( 4 5 ^{\circ} )}

tan (\frac{π}{4}) - sin (\frac{π}{6})

sec (- 31 0^{\circ})

15 sin (2 5^{\circ})

What is the value of 2(cos((3pi)/4)+isin((3pi)/4)) ?
The value of 2(cos((3pi)/4)+isin((3pi)/4)) is -sqrt(2)+sqrt(2)i