Help with imaginary numbers?

Question

Write each expression in the form a + bi

1. 5/i

2. i + i^2 + i^3 + i^4 + i^5

3. i ^ -3

4. √-50 - √-8

5. (2+3i)^2

6. 4(3+2i) - 5(1-i)

Answer 1

1) multiply top and bottom of expression by i and since i * i = -1 you now have -5i  or 0 - 5i  to put it in the form you are looking for

2) similarly i^2 = -1,  i^3 = -i, i^4 = 1 and i^5 = i  so your expression becomes  i + (-1) + (-i) + 1 + i = i

Answer 2

1.  (5/i)(i/i) = 5i/(i^2) = -5i

2.  i + i^2 + i^3 + i^4 + i^5 = i -1 - i + 1 + i = i

3.  i^-3 = 1/i^3 = 1 / (-i) = -(1/i)(i/i) = -i/(i^2) = -i/(-1) = i

4.  Ã¢ÂˆÂš-50 - √-8  = √(50)√(-1) - √(8)√(-1)

      = √(25)√(2)i - √(4)√(2)i = 5√(2)i - 2√(2) i = 3√(2) i

5.  (2 + 3i)(2 + 3i) = 4 + 6i + 6i + 9i^2 = 4 + 12i - 9 = -5 + 12i

5.  = 12 + 8i - 5 + 5i = 7 + 13i

Hope that helps.

--David

Answer 3

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