How do you write the following quotient in standard form 2+i2−i?

Question

recoronarrv · Accepted Answer

My preferred way to divide complex numbers is to multiply numerator and denominator by the complex conjugate of the denominator and then simplify.
Given:

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

Multiply numerator and denominator by the complex conjugate of the denominator:

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

The denominator becomes the difference of two squares:

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

Use the F.O.I.L method to multiply the the numerator:

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

Replace

i^{2} with - 1

:

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

Combine like terms:

\frac{3 + 4 i}{5}

Convert do

a + b i

form:

\frac{3}{5} + \frac{4}{5} i

Suhadolahbb · Accepted Answer

Reminder i2=(−1)2=−1  before dividing the complex numbers we require the denominator to be real   this is achieved by multiplying the numerator/denominator by the complex conjugate of the denominator  Note (a+bi)(a−bi)=a2+b2← a real number  the conjugate has the same values of a and b with the opposite sign the conjugate of (2−i) is (2+i)   ⇒2+i2−i×(2+i)(2+i)=(2+i)(2+i)(2−i)(2+i)  expanding numerator/denominator gives  4+4i+i24−i2=3+4i5  ⇒2+i2−i=35+45i← in standard form

How do you write the following quotient in standard form

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