Thread: complex numbers-solving equations

i don't know how to put these equations into perfect squares so i can get the complex number to put on the Argand diagram
(^ means 'to the power of' because i don't know how to use small letters)

1. 2x^(2)-7x+9=0
2. z^(3)-3z^(2)+z+5=0

and theres something else in the text book that doesnt make sense to me.
it says....
Determine the values of x and y by equating real and imaginary parts

1. x+3i=2-iy
2. 3x+i(y+1)=6+3i


can someone please try to solve these step by step so i know how you did them.... thanks!

Originally Posted by wish_i_was_a_maths_geek

i don't know how to put these equations into perfect squares so i can get the complex number to put on the Argand diagram
(^ means 'to the power of' because i don't know how to use small letters)

1. 2x^(2)-7x+9=0 Mr F says: Just use the quadratic formula.

2. z^(3)-3z^(2)+z+5=0 Mr F says: Consider p(z) = z^3 - 3z^2 + z + 5. Note that p(-1) = 0. Therefore z + 1 is a factor. So you have (z + 1)(z^2 - 4z + 5) = 0 ....

and theres something else in the text book that doesnt make sense to me.
it says....
Determine the values of x and y by equating real and imaginary parts

1. x+3i=2-iy Mr F says: Real parts equal => x = 2. Imaginary parts equal => 3 = -y.

2. 3x+i(y+1)=6+3i Mr F says: Real parts equal => 3x = 6. Imaginary parts equal => y + 1 = 3.


can someone please try to solve these step by step so i know how you did them.... thanks!

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