Questions: Simplify the expression and write the result in standard form, (a+bi). [ frac8+3i22= ]

$Simplify the expression and write the result in standard form, (a+bi). [ frac8+3i22= ]$

Transcript text: Simplify the expression and write the result in standard form, $a+b i$. \[ \frac{8+3 i}{22}= \] $\square$

Solution

Solution Steps

To simplify the expression $\frac{8+3i}{22}$ and write it in standard form $a + bi$, we need to divide both the real and imaginary parts of the numerator by the denominator. This will give us the real part $a$ and the imaginary part $b$.

Step 1: Divide the Real Part by the Denominator

To simplify the expression $\frac{8+3i}{22}$, we first divide the real part of the numerator by the denominator: \[ a = \frac{8}{22} = \frac{4}{11} \approx 0.3636 \]

Step 2: Divide the Imaginary Part by the Denominator

Next, we divide the imaginary part of the numerator by the denominator: \[ b = \frac{3}{22} \approx 0.1364 \]