SOLUTION: What is an equivalent form of 2/3+i?

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Question 389503: What is an equivalent form of 2/3+i?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
To remove i-terms on the denominator, you multiply above and below by the complex conjugate of the denominator (in this case %283-i%29):
2+%2F+%283+%2B+i%29+=+2+%2F+%283+%2B+i%29+%2A+%283+-+i%29%2F%283+-+i%29
= 2%283+-+i%29+%2F+%283+%2B+i%29%283+-+i%29
= 2%283+-+i%29+%2F+%283%5E2+-i%5E2%29
= 2%283+-+i%29+%2F+%283%5E2+%2B1%29+[ take extreme care with -i^2]
= 2%283+-+i%29+%2F+10
= %283+-+i%29+%2F+5