Multiply the numerator and denominator of <math><mstyle displaystyle="true"><mfrac><mrow><mn>4</mn><mi>i</mi></mrow><mrow><mn>1</mn><mo>+</mo><mn>1</mn><mi>i</mi></mrow></mfrac></mstyle></math> by the conjugate of <math><mstyle displaystyle="true"><mn>1</mn><mo>+</mo><mn>1</mn><mi>i</mi></mstyle></math> to make the denominator real.

Combine.

Simplify the numerator.

Apply the distributive property.

Multiply <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mn>4</mn><mi>i</mi><mrow><mo>(</mo><mo>-</mo><mi>i</mi><mo>)</mo></mrow></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> .

Raise <math><mstyle displaystyle="true"><mi>i</mi></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Raise <math><mstyle displaystyle="true"><mi>i</mi></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Use the power rule <math><mstyle displaystyle="true"><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi></mrow></msup><msup><mrow><mi>a</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>=</mo><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi><mo>+</mo><mi>n</mi></mrow></msup></mstyle></math> to combine exponents.

Add <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Simplify each term.

Rewrite <math><mstyle displaystyle="true"><msup><mrow><mi>i</mi></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> as <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>4</mn></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> .

Reorder <math><mstyle displaystyle="true"><mn>4</mn><mi>i</mi></mstyle></math> and <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> .

Simplify the denominator.

Expand <math><mstyle displaystyle="true"><mrow><mo>(</mo><mn>1</mn><mo>+</mo><mn>1</mn><mi>i</mi><mo>)</mo></mrow><mrow><mo>(</mo><mn>1</mn><mo>-</mo><mi>i</mi><mo>)</mo></mrow></mstyle></math> using the FOIL Method.

Apply the distributive property.

Apply the distributive property.

Apply the distributive property.

Simplify.

Multiply <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Raise <math><mstyle displaystyle="true"><mi>i</mi></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Use the power rule <math><mstyle displaystyle="true"><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi></mrow></msup><msup><mrow><mi>a</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>=</mo><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi><mo>+</mo><mi>n</mi></mrow></msup></mstyle></math> to combine exponents.

Add <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Add <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn><mi>i</mi></mstyle></math> and <math><mstyle displaystyle="true"><mn>1</mn><mi>i</mi></mstyle></math> .

Add <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Simplify each term.

Rewrite <math><mstyle displaystyle="true"><msup><mrow><mi>i</mi></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> as <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> .

Add <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>4</mn><mi>i</mi></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>2</mn><mrow><mo>(</mo><mn>2</mn><mo>)</mo></mrow><mo>+</mo><mn>2</mn><mrow><mo>(</mo><mn>2</mn><mi>i</mi><mo>)</mo></mrow></mstyle></math> .

Cancel the common factors.

Factor <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

Divide <math><mstyle displaystyle="true"><mn>2</mn><mo>+</mo><mn>2</mn><mi>i</mi></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Do you know how to Rewrite in Standard Form (4i)/(1+i)? If not, you can write to our math experts in our application. The best solution for your task you can find above on this page.

Name | seven hundred million eight hundred fifty-nine thousand two hundred sixty-eight |
---|

- 700859268 has 32 divisors, whose sum is
**1759151520** - The reverse of 700859268 is
**862958007** - Previous prime number is
**251**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 45
- Digital Root 9

Name | one hundred sixty-four million nine hundred forty thousand four hundred four |
---|

- 164940404 has 8 divisors, whose sum is
**371115918** - The reverse of 164940404 is
**404049461** - Previous prime number is
**2**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 32
- Digital Root 5

Name | two billion forty-eight million nine hundred seventy-three thousand seven hundred thirty-seven |
---|

- 2048973737 has 16 divisors, whose sum is
**2230617600** - The reverse of 2048973737 is
**7373798402** - Previous prime number is
**577**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 50
- Digital Root 5