Question

Help please.
Simplify: 2 + 3i / 4 + 2i

Answer 1

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`\displaystyle (7 + 4i)/(10)`

Explanation:

`\displaystyle (2 + 3i)/(4 + 2i) → (2 + 3i[4 - 2i])/(4 + 2i[4 - 2i]) = (14 + 8i)/(20) = \boxed{(7)/(10) + (2)/(5)i}`

When dividing complex numbers, multiply the denominatour and numeratour by the conjugate of the denominatour. Then simply towards the end.

* Here is something you should know:

`\displaystyle √(-1) = i \\ -1 = i^2 \\ -i = i^3 \\ 1 = i^4\: [every\:multiple\:of\:four]`

I am joyous to assist you at any time.