SOLUTION: Hello, I have a few problems on complex numbers that I don't understand how to solve them. Could you please help me on these problems? Thank you very much. problem 1: 3/sqrt2-5

Question 99744: Hello, I have a few problems on complex numbers that I don't understand how to solve them. Could you please help me on these problems? Thank you very much.
problem 1: 3/sqrt2-5i (i is for imaginary number)
problem 2: divide (1+i) by (2-i). Write the result in standard form. (i is for imaginary number)
problem 3: perform the operation and write the result in standard form: (5-sqrt4)^2

Thank you again,
Kumi
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
problem 1: 3/sqrt2-5i (i is for imaginary number)
= (3(sqrt(2)+5i)/[sqrt(2)-5i)(sqrt(2)+5i)]
= [3(sqrt(2)+5i)] / [2+25]
= (sqrt(2)+5i)/9
= (1/9)sqrt(2)+(5/9)i
------------------------------------
problem 2: divide (1+i) by (2-i). Write the result in standard form. (i is for imaginary number)
(1+i)/(2-i)
= [(1+i)(2+i)]/[(2-i)(2+i)]
= [1+3i]/[4+1]
= (1/5)+(3/5)i
--------------------------------

problem 3: perform the operation and write the result in standard form:
(5-sqrt4)^2
= 25+4 -2*5*sqrt4
= 29 - 20
= 9
============================
Cheers,
Stan H.

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