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, -, x, / Complex Numbers...

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, -, x, / Complex Numbers...

I'm having some trouble figuring out what steps I need to take to answer some harder questions.

Simplify
a) (2-i)(1+2i)(1-i)
Answer:7-i
b) (sqrt of 2/2 + sqrt of 2 /2i)^2
=i
c)(6-4i)^2 - (1-3i)^2 + 5i
=28-37i
d) sqrt of -4 + sqrt of -25
= 7i, -3i, 3i, or -7i
next the instructions say...

For each pair of roots, find a quadratic equation. Express your equation in the form ax^2+ bx + c =0.

a) -1/2 + sqrt of 3/2i, -1/2 - sqrt of 3/2i
=19+80i

thanx for the help...
1 REPLY 1

I'll do one. There others are about the same. Just be careful and systematic.

(2-i)(1+2i)(1-i)

Take it two pieces at a time.

[(2-i)(1+2i)](1-i)

[2 + 4i - i - 2*i2](1-i)
[2 + (4i - i) - 2*(i2)](1-i)
[2 + 3i - 2*(-1)](1-i)
[2 + 3i + 2](1-i)
[2 + 2 + 3i](1-i)
[(2 + 2) + 3i](1-i)
(4 + 3i)(1-i)

Now the new piece with the other original piece.

(4 + 3i)(1-i)
4 - 4i + 3i - 3*i2
4 - (4i - 3i) - 3*(i2)
4 - (i) - 3*(-1)
4 - i + 3
4 + 3 - i
(4 + 3) - i
7 - i

There it is.
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