Simplify 1/(2-i)

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Trigonometry

Simplify 1/(2-i)

$\frac{1}{2 - i}$

Multiply the numerator and denominator of $\frac{1}{2 - i}$ by the conjugate of $2 - i$ to make the denominator real.

$\frac{1}{2 - i} \cdot \frac{2 + i}{2 + i}$

Multiply.

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Combine.

$\frac{1 (2 + i)}{(2 - i) (2 + i)}$

Multiply $2 + i$ by $1$ .

$\frac{2 + i}{(2 - i) (2 + i)}$

Simplify the denominator.

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Expand $(2 - i) (2 + i)$ using the FOIL Method.

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Apply the distributive property.

$\frac{2 + i}{2 (2 + i) - i (2 + i)}$

Apply the distributive property.

$\frac{2 + i}{2 \cdot 2 + 2 i - i (2 + i)}$

Apply the distributive property.

$\frac{2 + i}{2 \cdot 2 + 2 i - i \cdot 2 - i i}$

Simplify.

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Multiply $2$ by $2$ .

$\frac{2 + i}{4 + 2 i - i \cdot 2 - i i}$

Multiply $2$ by $- 1$ .

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

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

$\frac{2 + i}{4 + 2 i - 2 i - (i^{1} i)}$

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

$\frac{2 + i}{4 + 2 i - 2 i - (i^{1} i^{1})}$

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

$\frac{2 + i}{4 + 2 i - 2 i - i^{1 + 1}}$

Add $1$ and $1$ .

$\frac{2 + i}{4 + 2 i - 2 i - i^{2}}$

Subtract $2 i$ from $2 i$ .

$\frac{2 + i}{4 + 0 - i^{2}}$

Add $4$ and $0$ .

$\frac{2 + i}{4 - i^{2}}$

Simplify each term.

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

$\frac{2 + i}{4 - - 1}$

Multiply $- 1$ by $- 1$ .

$\frac{2 + i}{4 + 1}$

Add $4$ and $1$ .

$\frac{2 + i}{5}$

Split the fraction $\frac{2 + i}{5}$ into two fractions.

$\frac{2}{5} + \frac{i}{5}$

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Name

Name	one billion five hundred eighty-nine million nine hundred thirty-nine thousand five hundred twenty-eight

Interesting facts

1589939528 has 32 divisors, whose sum is 5368642524
The reverse of 1589939528 is 8259399851
Previous prime number is 2113

Basic properties

Is Prime? no
Number parity even
Number length 10
Sum of Digits 59
Digital Root 5

Name

Name	two hundred nine million four hundred ninety-six thousand six hundred seventy-six

Interesting facts

209496676 has 16 divisors, whose sum is 471497796
The reverse of 209496676 is 676694902
Previous prime number is 7237

Basic properties

Is Prime? no
Number parity even
Number length 9
Sum of Digits 49
Digital Root 4

Name

Name	one billion one hundred seventy-four million two hundred ninety-one thousand five hundred sixty-one

Interesting facts

1174291561 has 4 divisors, whose sum is 1236096400
The reverse of 1174291561 is 1651924711
Previous prime number is 19

Basic properties

Is Prime? no
Number parity odd
Number length 10
Sum of Digits 37
Digital Root 1

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