simplify (4+3i)/(3-2i) — step-by-step solution | Explain MAths

simplify (4+3i)/(3-2i)

Let's reduce:

\frac{4 + 3 i}{3 - 2 i}

Multiply numerator and denominator by the conjugate

3 + 2 i

; (a+bi)(a-bi)=a²+b²

\frac{(4 + 3 i) \times (3 + 2 i)}{3^{2} + {(-2)}^{2}}

ℹ

3^{2}

=

9

‖

{(-2)}^{2}

=

4

\frac{(4 + 3 i) \times (3 + 2 i)}{9 + 4}

\frac{(4 + 3 i) \times (3 + 2 i)}{13}

\frac{4 \times 3 + 4 \times 2 i + 3 \times i \times 3 + 3 \times i \times 2 \times i}{13}

ℹ

4 \times 3

=

12

‖

4 \times 2

=

8

‖

3 \times 3

=

9

‖

3 \times 2

=

6

‖

i \times i

=

i^{2}

\frac{12 + 8 i + 9 i + 6 i^{2}}{13}

ℹ

8 i + 9 i

=

17 i

‖

6 \times (-1)

=

-6

‖

i^{2}

=

-1

\frac{12 + 17 i - 6}{13}

▶Simplified form:

\frac{6 + 17 i}{13}

The numeric value of:

\frac{6 + 17 i}{13}

is:

\frac{6}{13} + \frac{17}{13} \times i

▷

\approx 0.4615 + \approx 1.3077 i