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Solving equations in complex numbers

Solving equations in complex numbers

IB Year 6 | Grade 12

Find the real numbers \(x\) and \(y\) if

  1. \(x(2-3i)+y(4+5i)=2-14i\)
  2. \((x+iy)^2=3+4i\)
  3. \((x+iy)^2=\frac{50}{4+3i}\)
  4. \((2x+3y)-x^3i=14-64i\)

Solution:

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Answer:(a) \((x,y)=(3,-1)\). (b) \((2,1)\) or \((-2,-1)\). (c) \((3,-1)\) or \((-3,1)\). (d) \((4,2)\).

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