Find the Reciprocal ( square root of 3)/2+( square root of 3)/2i

$\frac{\sqrt{3}}{2} + \frac{\sqrt{3}}{2} i$

Step 1

To find the reciprocal, divide $1$ by the number given.

$\frac{1}{\frac{\sqrt{3}}{2} + \frac{\sqrt{3}}{2} \cdot i}$

Step 2

Simplify.

Multiply the numerator and denominator of $\frac{1}{0.8660254 + 0.8660254 \cdot i}$ by the conjugate of $0.8660254 + 0.8660254 \cdot i$ to make the denominator real.

$\frac{1}{0.8660254 + 0.8660254 \cdot i} \cdot \frac{0.8660254 - 0.8660254 i}{0.8660254 - 0.8660254 i}$

Multiply.

Combine.

$\frac{1 (0.8660254 - 0.8660254 i)}{(0.8660254 + 0.8660254 \cdot i) (0.8660254 - 0.8660254 i)}$

Multiply $0.8660254 - 0.8660254 i$ by $1$ .

$\frac{0.8660254 - 0.8660254 i}{(0.8660254 + 0.8660254 \cdot i) (0.8660254 - 0.8660254 i)}$

Simplify the denominator.

Expand $(0.8660254 + 0.8660254 \cdot i) (0.8660254 - 0.8660254 i)$ using the FOIL Method.

Apply the distributive property.

$\frac{0.8660254 - 0.8660254 i}{0.8660254 (0.8660254 - 0.8660254 i) + 0.8660254 \cdot i (0.8660254 - 0.8660254 i)}$

Apply the distributive property.

$\frac{0.8660254 - 0.8660254 i}{0.8660254 \cdot 0.8660254 + 0.8660254 (- 0.8660254 i) + 0.8660254 \cdot i (0.8660254 - 0.8660254 i)}$

Apply the distributive property.

$\frac{0.8660254 - 0.8660254 i}{0.8660254 \cdot 0.8660254 + 0.8660254 (- 0.8660254 i) + 0.8660254 \cdot i \cdot 0.8660254 + 0.8660254 \cdot i (- 0.8660254 i)}$

Simplify.

Multiply $0.8660254$ by $0.8660254$ .

$\frac{0.8660254 - 0.8660254 i}{0.75 + 0.8660254 (- 0.8660254 i) + 0.8660254 \cdot i \cdot 0.8660254 + 0.8660254 \cdot i (- 0.8660254 i)}$

Multiply $- 0.8660254$ by $0.8660254$ .

$\frac{0.8660254 - 0.8660254 i}{0.75 - 0.75 i + 0.8660254 \cdot i \cdot 0.8660254 + 0.8660254 \cdot i (- 0.8660254 i)}$

Multiply $0.8660254$ by $0.8660254$ .

$\frac{0.8660254 - 0.8660254 i}{0.75 - 0.75 i + 0.75 \cdot i + 0.8660254 \cdot i (- 0.8660254 i)}$

Multiply $- 0.8660254$ by $0.8660254$ .

$\frac{0.8660254 - 0.8660254 i}{0.75 - 0.75 i + 0.75 \cdot i - 0.75 \cdot i i}$

Raise $i$ to the power of $1$ .

$\frac{0.8660254 - 0.8660254 i}{0.75 - 0.75 i + 0.75 \cdot i - 0.75 \cdot (i^{1} i)}$

Raise $i$ to the power of $1$ .

$\frac{0.8660254 - 0.8660254 i}{0.75 - 0.75 i + 0.75 \cdot i - 0.75 \cdot (i^{1} i^{1})}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{0.8660254 - 0.8660254 i}{0.75 - 0.75 i + 0.75 \cdot i - 0.75 \cdot i^{1 + 1}}$

Add $1$ and $1$ .

$\frac{0.8660254 - 0.8660254 i}{0.75 - 0.75 i + 0.75 \cdot i - 0.75 \cdot i^{2}}$

Add $- 0.75 i$ and $0.75 \cdot i$ .

$\frac{0.8660254 - 0.8660254 i}{0.75 + 0 i - 0.75 \cdot i^{2}}$

Simplify each term.

Multiply $0$ by $i$ .

$\frac{0.8660254 - 0.8660254 i}{0.75 + 0 - 0.75 \cdot i^{2}}$

Rewrite $i^{2}$ as $- 1$ .

$\frac{0.8660254 - 0.8660254 i}{0.75 + 0 - 0.75 \cdot - 1}$

Multiply $- 0.75$ by $- 1$ .

$\frac{0.8660254 - 0.8660254 i}{0.75 + 0 + 0.75}$

Add $0.75$ and $0$ .

$\frac{0.8660254 - 0.8660254 i}{0.75 + 0.75}$

Add $0.75$ and $0.75$ .

$\frac{0.8660254 - 0.8660254 i}{1.5}$

Rewrite $0.8660254$ as $1 (0.8660254)$ .

$\frac{1 (0.8660254) - 0.8660254 i}{1.5}$

Factor $1$ out of $- 0.8660254 i$ .

$\frac{1 (0.8660254) + 1 (- 0.8660254 i)}{1.5}$

Factor $1$ out of $1 (0.8660254) + 1 (- 0.8660254 i)$ .

$\frac{1 (0.8660254 - 0.8660254 i)}{1.5}$

Factor $1.5$ out of $1.5$ .

$\frac{1 (0.8660254 - 0.8660254 i)}{1.5 (1)}$

Separate fractions.

$\frac{1}{1.5} \cdot \frac{0.8660254 - 0.8660254 i}{1}$

Simplify the expression.

Divide $1$ by $1.5$ .

$0.66666666 \frac{0.8660254 - 0.8660254 i}{1}$

Divide $0.8660254 - 0.8660254 i$ by $1$ .

$0.66666666 (0.8660254 - 0.8660254 i)$

Apply the distributive property.

$0.66666666 \cdot 0.8660254 + 0.66666666 (- 0.8660254 i)$

Multiply.

Multiply $0.66666666$ by $0.8660254$ .

$0.57735026 + 0.66666666 (- 0.8660254 i)$

Multiply $- 0.8660254$ by $0.66666666$ .

$0.57735026 - 0.57735026 i$

Find the Reciprocal ( square root of 3)/2+( square root of 3)/2i

Related Questions

Support LCMGCF.com by disabling your adblocker.