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Algebra2

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I got this answer for a problem, and I'm not sure if it's right.
Can someone tell me if I'm correct?
1.(2+4i / 3-i)
= 6/7+5/7i

  • Algebra2 -

    2+41 /(3-i)
    rationalize
    (2+4i)(3+i)/10= (6+2i+12i-4)/10=
    =(2+14i)/10

  • Algebra2 -

    Ahh!
    I'm confused about this math stuff:/
    it's my first time trying these algebra problems.
    I'm trying to go by the teacher's examples.
    Can You tell me if these are right:p?
    2. (7-√-15)^2
    = 34+14i√15i

    3.4+√-20 / 2
    =2+2.5√4i

  • Algebra2 -

    another way, in polar form:

    (2+4i)=sqrt20@arctan2
    (3-i)=sqrt10@arctan(-1/3)

    so (2+4i)/(3-i)=sqrt20/sqrt10 @ (arctan2-arctan-1/3)=sqrt2 @(1.11rad-(-.321))
    = sqrt2 @1.43rad=sqrt2 @ 81.9 deg

    Now converting this (only to compare with the above)
    = sqrt2 (cos81.9+isin81.9)
    = (.198+i*1.40)
    and the above is .2+i1.40

    I rounded the angles on the arctan conversions...

  • Algebra2 -

    2. (7-√-15)^2
    = 34+14i√15i ????

    (7-isqrt15)^2=49-15-2isqrt15=34-2i sqrt15

    3.4+√-20 / 2
    =2+2.5√4i ????

    4/2+1/2 i sqrt20=2+.5i*sqrt4*sqrt5
    = 2+i sqrt5

  • Algebra2 -

    (7-isqrt15)^2=49-15-2isqrt15??
    I get 49-15- 14√15 i

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