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Math

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Write each complex number in rectangular form?

I need help with this. :/

2(cos120°+i sin 120°)

and

4(cos 7π/4 + i sin 7π/4)

?

  • Math - ,

    2*cos120 + i2*sin120.

    X = hor = 2*cos120 = -1.
    Y = VER = 2*sin120 = 1.732.

    tanA = Y/X = 1.732/-1 = -1.732,
    A = -60 deg = 300 deg CCW.

    R = X/cosA = = -1/cos300 = -2 = Resultant.

    R = -2 @ -60 deg = -2 @ 300 deg CCW.

    4*cos7pi/4 + i4*sin7pi/4,

    7pi/4 = 7*180/4 = 315 deg.
    X = hor = 4*cos315 = 2.83.
    Y = ver = 4*sin315 = -2.83.

    tanA = Y/X = -2.83/2.83 = -1.
    A = -45 deg = 315 deg CCW.

    R = X/cosA = 2.83/cos315 = 4.0 = Resultant.

    R = 4.0 @ -45 deg = 4.0 @ 315 deg CCW = Resultant.

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