Question

Write the expression in standard form. three divided by quantity three minus twelve i.

Answer 1

3/(3 - 12i)

To simplify this, multiply both sides by (3 + 12i)

(3 - 12i)(3 + 12i)

Distributive property.

3(3 + 12i) - 12i(3 + 12i)

9 + 36i - 36i - 144i^2

Simplify.

9 - 144i^2

i^2 can be interpreted as -1.

9 + 144

Combine like terms.

153 is the simplified version of the bottom half of the expression.

Now for the top half.

3(3 + 12i)

Distributive property.

9 + 36i

We can simplify this further by factoring.

3(3 + 12i)/153

1 + 4i/17

1/17 + 4i/17 is the simplified version of the expression. (This is your answer.)

Let me know if you have any other questions.