QuestionDivide $\frac{-3-4 i}{2 i}$ and express the answer as $a + bi$ .

Studdy Solution

STEP 1

Assumptions1. We are asked to divide $\frac{-3-4 i}{ i}$ . . We want to write the result in the form $a+bi$ , where $a$ and $b$ are real numbers.

STEP 2

First, we can simplify the expression by multiplying the numerator and the denominator by the conjugate of the denominator. The conjugate of a complex number $a+bi$ is $a-bi$ . So, the conjugate of $2i$ is $-2i$ .
$\frac{--4 i}{2 i} \times \frac{-2i}{-2i}$

STEP 3

Now, multiply the numerator and the denominator.
$\frac{(-3- i) \times -2i}{(2 i) \times -2i}$

STEP 4

implify the numerator and the denominator.
$\frac{6i+8 i^2}{-4 i^2}$

STEP 5

Remember that $i^2$ is equal to $-1$ . Substitute $i^2$ with $-1$ .
$\frac{i+8(-1)}{-4(-1)}$

STEP 6

implify the expression.
$\frac{6i-8}{4}$

STEP 7

Divide each term in the numerator by the denominator.
$\frac{6i}{4}-\frac{}{4}$

STEP 8

implify each term.
$1.5i-2$

STEP 9

The final result is in the form $a+bi$ . However, the real part should be written first. So, we rewrite the result as $-2+.5i$ .
The result of the division is $-2+.5i$ .

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