Example Question 1

Example corresponding to question 1 in college algebra 2.

Example 1


$z$ is a complex number and $\bar z$ its conjugate such that $4z-2 \bar z = 4 -18i$. What is z?

  1. $2-9i$
  2. $2$
  3. $-9i$
  4. $2-3i$
  5. $2+3i$

Solution


  1. We need to solve the given equation in order to find the complex number $z$. Let us first write $z$ in the standard form of complex numbers:

    $z=a+bi$ , where $a$ and $b$ are real numbers.


  2. The complex conjugate $\bar z$ is defined as follows

    $\bar z = a - bi$

  3. We now substitute $z$ and $\bar z$ in the given equation by $a+bi$ and $a - bi$ to write

    $4(a+bi)-2(a-bi) = 4 -18i$

  4. Expand and group real terms and imaginary terms

    $4a + 4bi -2a + 2bi=4-18i$

    $2a+6bi=4-18i$

  5. Complex numbers are equal if they have equal real parts and equal imaginary parts. Hence

    $2a = 4$ and $6b = -18$

  6. Solve for $a$ and $b$ to obtain

    $a = 2$ and $b = -3$ and $z=2-3i$

    Answer D

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