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Math Help - complex numbers

  1. #1
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    complex numbers

    I am having trouble with these 2 questions

    Find the complex number z such that (5+2i)+ ((−3−2i)/z)=5i

    and

    Find the complex number z such that (2−2i)z+(1−4i)z bar=4+5i

    any help would be great
    thanks
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  2. #2
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    Quote Originally Posted by kblythe View Post
    I am having trouble with these 2 questions

    Find the complex number z such that (5+2i)+ ((−3−2i)/z)=5i

    and

    Find the complex number z such that (2−2i)z+(1−4i)z bar=4+5i

    any help would be great
    thanks
    1) \frac{-3 - 2i}{z} = 3i - 5 \Rightarrow \frac{z}{-3 - 2i} = \frac{1}{-5 + 3i} \Rightarrow z = \frac{-3 - 2i}{-5 + 3i}. Your job is to express this answer in cartesian form.

    2) Let z = x + iy:

    (2 - 2i)(x + iy) + (1 - 4i)(x - iy) = 4 + 5i.

    Expand and equate the real and imaginary parts on each side. This will give you two simultaneous equations that you must solve for x and y.

    If you need more help, please show all your work and say where you're stuck.
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