Question

REALLY NEED HELP!
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Answer 1

14. 12/13 -8/13i

15. 5

Explanation:

14. Multiply the fraction by the conjugate of the denominator divided by itself.

`=(0-4i)/(2-3i)=(-4i(2+3i))/((2-3i)(2+3i))=(-8i-12i^2)/(2^2-(3i)^2)\\\\=(12-8i)/(4+9)=(12)/(13)-(8)/(13)i`

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15 (1-2i)(1+2i) = (1)² -(2i)² = 1 -(-4) = 1+4 = 5

It can be useful to remember that z·z* = Re(z)² +Im(z)². Since the parts are squared, signs can be ignored (magnitudes used).