# Convert to Trigonometric Form -1/(1+i)

Convert to Trigonometric Form -1/(1+i)
Multiply the numerator and denominator of by the conjugate of to make the denominator real.
Multiply.
Combine.
Multiply by .
Simplify the denominator.
Expand using the FOIL Method.
Apply the distributive property.
Apply the distributive property.
Apply the distributive property.
Simplify.
Multiply by .
Multiply by .
Multiply by .
Multiply by .
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Simplify each term.
Rewrite as .
Multiply by .
Split the fraction into two fractions.
Move the negative in front of the fraction.
Apply the distributive property.
Multiply .
Multiply by .
Multiply by .
This is the trigonometric form of a complex number where is the modulus and is the angle created on the complex plane.
The modulus of a complex number is the distance from the origin on the complex plane.
where
Substitute the actual values of and .
Find .
Apply the product rule to .
One to any power is one.
Raise to the power of .
Use the power rule to distribute the exponent.
Apply the product rule to .
Apply the product rule to .
Raise to the power of .
Multiply by .
One to any power is one.
Raise to the power of .
Combine the numerators over the common denominator.
Cancel the common factor of and .
Factor out of .
Cancel the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Rewrite as .
Any root of is .
Multiply by .
Combine and simplify the denominator.
Multiply and .
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Rewrite as .
Use to rewrite as .
Apply the power rule and multiply exponents, .
Combine and .
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Evaluate the exponent.
The angle of the point on the complex plane is the inverse tangent of the complex portion over the real portion.
Since inverse tangent of produces an angle in the second quadrant, the value of the angle is .
Substitute the values of and .
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### Name

Name one billion seven hundred eighty-three million eight hundred thirteen thousand two hundred sixty-three

### Interesting facts

• 1783813263 has 8 divisors, whose sum is 2378688000
• The reverse of 1783813263 is 3623183871
• Previous prime number is 10399

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 10
• Sum of Digits 42
• Digital Root 6

### Name

Name one billion sixty-two million eight hundred sixty-seven thousand one hundred twenty-eight

### Interesting facts

• 1062867128 has 32 divisors, whose sum is 3588178824
• The reverse of 1062867128 is 8217682601
• Previous prime number is 4013

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 41
• Digital Root 5

### Name

Name one billion thirty-two million four hundred nine thousand two hundred twenty-seven

### Interesting facts

• 1032409227 has 4 divisors, whose sum is 1376545640
• The reverse of 1032409227 is 7229042301
• Previous prime number is 3

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 10
• Sum of Digits 30
• Digital Root 3