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How do you simplify # (2+2i)/(1+2i) # and write in a+bi form?

Answer 1

Serenity Johnson

Multiply the numerator and denominator by the complex conjugate of the denominator to find

#(2+2i)/(1+2i)=6/5 - 2/5i#

Given a complex number #a+bi# with #a,b in RR# we have

#(a+bi)(a-bi) = a^2 + b^2#

#a-bi# is called the complex conjugate (or conjugate) of #a+bi#. Using this:

#(2+2i)/(1+2i) = (2+2i)/(1+2i)*(1-2i)/(1-2i)#

#= ((2+2i)(1-2i))/(1^2 + 2^2)#

#= (6-2i)/5#

#=6/5 - 2/5i#

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Answer 2

Benjamin Achtenberg

To simplify (2+2i)/(1+2i) and write it in a+bi form, you can multiply the numerator and denominator by the conjugate of the denominator, which is (1-2i). Then, perform the multiplication, combine like terms, and express the result in the form a+bi.

The simplified expression in a+bi form is:

(2+2i)/(1+2i) = (2+2i)(1-2i)/(1+2i)(1-2i) = (2-4i+2i-4i^2)/(1-2i+2i-4i^2) = (2-4i+2i+4)/(1+4) = (6-2i)/5

Therefore, (2+2i)/(1+2i) simplified and written in a+bi form is (6-2i)/5.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.