Solve in Terms of the Arbitrary Variable u u=(1+i square root of 3) v=(1-i square root of 3)

$u = (1 + i \sqrt{3})$ $v = (1 - i \sqrt{3})$

Step 1

Remove parentheses.

$v = 1 - (\frac{u \sqrt{3}}{3} - \frac{\sqrt{3}}{3}) \sqrt{3}$

$i = \frac{u \sqrt{3}}{3} - \frac{\sqrt{3}}{3}$

Step 2

Simplify $1 - (\frac{u \sqrt{3}}{3} - \frac{\sqrt{3}}{3}) \sqrt{3}$ .

Simplify each term.

Apply the distributive property.

$v = 1 + (- \frac{u \sqrt{3}}{3} + \frac{\sqrt{3}}{3}) \sqrt{3}$

$i = \frac{u \sqrt{3}}{3} - \frac{\sqrt{3}}{3}$

Multiply $- - \frac{\sqrt{3}}{3}$ .

Multiply $- 1$ by $- 1$ .

$v = 1 + (- \frac{u \sqrt{3}}{3} + 1 (\frac{\sqrt{3}}{3})) \sqrt{3}$

$i = \frac{u \sqrt{3}}{3} - \frac{\sqrt{3}}{3}$

Multiply $\frac{\sqrt{3}}{3}$ by $1$ .

$v = 1 + (- \frac{u \sqrt{3}}{3} + \frac{\sqrt{3}}{3}) \sqrt{3}$

$i = \frac{u \sqrt{3}}{3} - \frac{\sqrt{3}}{3}$

$v = 1 + (- \frac{u \sqrt{3}}{3} + \frac{\sqrt{3}}{3}) \sqrt{3}$

$i = \frac{u \sqrt{3}}{3} - \frac{\sqrt{3}}{3}$

Apply the distributive property.

$v = 1 - \frac{u \sqrt{3}}{3} \cdot \sqrt{3} + \frac{\sqrt{3}}{3} \cdot \sqrt{3}$

$i = \frac{u \sqrt{3}}{3} - \frac{\sqrt{3}}{3}$

Multiply $- \frac{u \sqrt{3}}{3} \sqrt{3}$ .

Combine $\sqrt{3}$ and $\frac{u \sqrt{3}}{3}$ .

$v = 1 - \frac{\sqrt{3} (u \sqrt{3})}{3} + \frac{\sqrt{3}}{3} \cdot \sqrt{3}$

$i = \frac{u \sqrt{3}}{3} - \frac{\sqrt{3}}{3}$

Raise $\sqrt{3}$ to the power of $1$ .

$v = 1 - \frac{u (\sqrt{3} \sqrt{3})}{3} + \frac{\sqrt{3}}{3} \cdot \sqrt{3}$

$i = \frac{u \sqrt{3}}{3} - \frac{\sqrt{3}}{3}$

Raise $\sqrt{3}$ to the power of $1$ .

$v = 1 - \frac{u (\sqrt{3} \sqrt{3})}{3} + \frac{\sqrt{3}}{3} \cdot \sqrt{3}$

$i = \frac{u \sqrt{3}}{3} - \frac{\sqrt{3}}{3}$

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

$v = 1 - \frac{u {\sqrt{3}}^{1 + 1}}{3} + \frac{\sqrt{3}}{3} \cdot \sqrt{3}$

$i = \frac{u \sqrt{3}}{3} - \frac{\sqrt{3}}{3}$

Add $1$ and $1$ .

$v = 1 - \frac{u {\sqrt{3}}^{2}}{3} + \frac{\sqrt{3}}{3} \cdot \sqrt{3}$

$i = \frac{u \sqrt{3}}{3} - \frac{\sqrt{3}}{3}$

$v = 1 - \frac{u {\sqrt{3}}^{2}}{3} + \frac{\sqrt{3}}{3} \cdot \sqrt{3}$

$i = \frac{u \sqrt{3}}{3} - \frac{\sqrt{3}}{3}$

Multiply $\frac{\sqrt{3}}{3} \sqrt{3}$ .

Combine $\frac{\sqrt{3}}{3}$ and $\sqrt{3}$ .

$v = 1 - \frac{u {\sqrt{3}}^{2}}{3} + \frac{\sqrt{3} \sqrt{3}}{3}$

$i = \frac{u \sqrt{3}}{3} - \frac{\sqrt{3}}{3}$

Raise $\sqrt{3}$ to the power of $1$ .

$v = 1 - \frac{u {\sqrt{3}}^{2}}{3} + \frac{\sqrt{3} \sqrt{3}}{3}$

$i = \frac{u \sqrt{3}}{3} - \frac{\sqrt{3}}{3}$

Raise $\sqrt{3}$ to the power of $1$ .

$v = 1 - \frac{u {\sqrt{3}}^{2}}{3} + \frac{\sqrt{3} \sqrt{3}}{3}$

$i = \frac{u \sqrt{3}}{3} - \frac{\sqrt{3}}{3}$

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

$v = 1 - \frac{u {\sqrt{3}}^{2}}{3} + \frac{{\sqrt{3}}^{1 + 1}}{3}$

$i = \frac{u \sqrt{3}}{3} - \frac{\sqrt{3}}{3}$

Add $1$ and $1$ .

$v = 1 - \frac{u {\sqrt{3}}^{2}}{3} + \frac{{\sqrt{3}}^{2}}{3}$

$i = \frac{u \sqrt{3}}{3} - \frac{\sqrt{3}}{3}$

$v = 1 - \frac{u {\sqrt{3}}^{2}}{3} + \frac{{\sqrt{3}}^{2}}{3}$

$i = \frac{u \sqrt{3}}{3} - \frac{\sqrt{3}}{3}$

Simplify each term.

Rewrite ${\sqrt{3}}^{2}$ as $3$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

$v = 1 - \frac{u {(3^{\frac{1}{2}})}^{2}}{3} + \frac{{\sqrt{3}}^{2}}{3}$

$i = \frac{u \sqrt{3}}{3} - \frac{\sqrt{3}}{3}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$v = 1 - \frac{u \cdot 3^{\frac{1}{2} \cdot 2}}{3} + \frac{{\sqrt{3}}^{2}}{3}$

$i = \frac{u \sqrt{3}}{3} - \frac{\sqrt{3}}{3}$

Combine $\frac{1}{2}$ and $2$ .

$v = 1 - \frac{u \cdot 3^{\frac{2}{2}}}{3} + \frac{{\sqrt{3}}^{2}}{3}$

$i = \frac{u \sqrt{3}}{3} - \frac{\sqrt{3}}{3}$

Cancel the common factor of $2$ .

Cancel the common factor.

$v = 1 - \frac{u \cdot 3^{\frac{2}{2}}}{3} + \frac{{\sqrt{3}}^{2}}{3}$

$i = \frac{u \sqrt{3}}{3} - \frac{\sqrt{3}}{3}$

Rewrite the expression.

$v = 1 - \frac{u \cdot 3}{3} + \frac{{\sqrt{3}}^{2}}{3}$

$i = \frac{u \sqrt{3}}{3} - \frac{\sqrt{3}}{3}$

$v = 1 - \frac{u \cdot 3}{3} + \frac{{\sqrt{3}}^{2}}{3}$

$i = \frac{u \sqrt{3}}{3} - \frac{\sqrt{3}}{3}$

Evaluate the exponent.

$v = 1 - \frac{u \cdot 3}{3} + \frac{{\sqrt{3}}^{2}}{3}$

$i = \frac{u \sqrt{3}}{3} - \frac{\sqrt{3}}{3}$

$v = 1 - \frac{u \cdot 3}{3} + \frac{{\sqrt{3}}^{2}}{3}$

$i = \frac{u \sqrt{3}}{3} - \frac{\sqrt{3}}{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

$v = 1 - \frac{u \cdot 3}{3} + \frac{{\sqrt{3}}^{2}}{3}$

$i = \frac{u \sqrt{3}}{3} - \frac{\sqrt{3}}{3}$

Divide $u$ by $1$ .

$v = 1 - u + \frac{{\sqrt{3}}^{2}}{3}$

$i = \frac{u \sqrt{3}}{3} - \frac{\sqrt{3}}{3}$

$v = 1 - u + \frac{{\sqrt{3}}^{2}}{3}$

$i = \frac{u \sqrt{3}}{3} - \frac{\sqrt{3}}{3}$

Rewrite ${\sqrt{3}}^{2}$ as $3$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

$v = 1 - u + \frac{{(3^{\frac{1}{2}})}^{2}}{3}$

$i = \frac{u \sqrt{3}}{3} - \frac{\sqrt{3}}{3}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$v = 1 - u + \frac{3^{\frac{1}{2} \cdot 2}}{3}$

$i = \frac{u \sqrt{3}}{3} - \frac{\sqrt{3}}{3}$

Combine $\frac{1}{2}$ and $2$ .

$v = 1 - u + \frac{3^{\frac{2}{2}}}{3}$

$i = \frac{u \sqrt{3}}{3} - \frac{\sqrt{3}}{3}$

Cancel the common factor of $2$ .

Cancel the common factor.

$v = 1 - u + \frac{3^{\frac{2}{2}}}{3}$

$i = \frac{u \sqrt{3}}{3} - \frac{\sqrt{3}}{3}$

Rewrite the expression.

$v = 1 - u + \frac{3}{3}$

$i = \frac{u \sqrt{3}}{3} - \frac{\sqrt{3}}{3}$

$v = 1 - u + \frac{3}{3}$

$i = \frac{u \sqrt{3}}{3} - \frac{\sqrt{3}}{3}$

Evaluate the exponent.

$v = 1 - u + \frac{3}{3}$

$i = \frac{u \sqrt{3}}{3} - \frac{\sqrt{3}}{3}$

$v = 1 - u + \frac{3}{3}$

$i = \frac{u \sqrt{3}}{3} - \frac{\sqrt{3}}{3}$

Divide $3$ by $3$ .

$v = 1 - u + 1$

$i = \frac{u \sqrt{3}}{3} - \frac{\sqrt{3}}{3}$

$v = 1 - u + 1$

$i = \frac{u \sqrt{3}}{3} - \frac{\sqrt{3}}{3}$

$v = 1 - u + 1$

$i = \frac{u \sqrt{3}}{3} - \frac{\sqrt{3}}{3}$

Add $1$ and $1$ .

$v = - u + 2$

$i = \frac{u \sqrt{3}}{3} - \frac{\sqrt{3}}{3}$

$v = - u + 2$

$i = \frac{u \sqrt{3}}{3} - \frac{\sqrt{3}}{3}$

Solve in Terms of the Arbitrary Variable u u=(1+i square root of 3) v=(1-i square root of 3)

Related Questions

Support LCMGCF.com by disabling your adblocker.