- #1
Trail_Builder
- 149
- 0
not sure if this is in the right section as i havn't got to calculus yet lol. anyways, was wondering whether you could check i have calculated this right as I'm learning complex numbers at the moment and have no way of checking my working. thnx
Calculate [tex](\surd5 - 2i)^{11}[/tex]
Find polar form of [tex](\surd5 - 2i)[/tex]
[tex]r = complex modulus[/tex]
[tex]r = \sqrt{5 + 4}[/tex]
[tex]r = 3[/tex]
[tex]Arg(z) = sin^{-1}(\frac{2}{3})[/tex]
sub all that into [tex]r(cosArg(z) + i*sinArg(z))[/tex]
but before actual calculate take the power of 11 into consideration so...
[tex](\surd5 - 2i)^{11} = r^{11}(11*cosArg(z) + 11i*sinArg(z))[/tex]
I then calculate all that as
[tex]177147(8.19..+7.33..i)[/tex]
[tex]1452413.3..+1299078i[/tex]
hope that's right :D
thnx
Homework Statement
Calculate [tex](\surd5 - 2i)^{11}[/tex]
Homework Equations
The Attempt at a Solution
Find polar form of [tex](\surd5 - 2i)[/tex]
[tex]r = complex modulus[/tex]
[tex]r = \sqrt{5 + 4}[/tex]
[tex]r = 3[/tex]
[tex]Arg(z) = sin^{-1}(\frac{2}{3})[/tex]
sub all that into [tex]r(cosArg(z) + i*sinArg(z))[/tex]
but before actual calculate take the power of 11 into consideration so...
[tex](\surd5 - 2i)^{11} = r^{11}(11*cosArg(z) + 11i*sinArg(z))[/tex]
I then calculate all that as
[tex]177147(8.19..+7.33..i)[/tex]
[tex]1452413.3..+1299078i[/tex]
hope that's right :D
thnx