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Simplify.\newline−4i−9i\frac{{-4i}}{{-9i}}\newline\newlineWrite your answer in the form a+bia + bi. Reduce all fractions.\newline_____\_\_\_\_\_\newline

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Q. Simplify.\newline−4i−9i\frac{{-4i}}{{-9i}}\newline\newlineWrite your answer in the form a+bia + bi. Reduce all fractions.\newline_____\_\_\_\_\_\newline
  1. Separate numbers and imaginary unit: Separate the numbers and the imaginary unit (ii). The expression (−4i)/(−9i)(-4i)/(-9i) can be written as (−4)/(−9)×i/i(-4)/(-9) \times i/i.
  2. Simplify negative fraction: Simplify the fraction (−4)/(−9)(-4)/(-9).\newlineSince both the numerator and the denominator are negative, they will cancel each other out, leaving us with a positive fraction.\newline(−4)/(−9)(-4)/(-9) simplifies to 4/94/9.
  3. Simplify imaginary unit: Simplify the imaginary unit fraction i/ii/i.\newlineThe imaginary unit ii divided by itself is just 11, because any non-zero number divided by itself equals 11.\newlinei/ii/i simplifies to 11.
  4. Multiply fractions: Multiply the simplified real fraction by the simplified imaginary unit fraction. 49×1\frac{4}{9} \times 1 equals 49.\frac{4}{9}.
  5. Write final answer: Write the final answer in the form a+bia + bi. Since there is no real part and the imaginary part is 49\frac{4}{9}, the final answer is 0+49i0 + \frac{4}{9}i.

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