Question

REALLY NEED HELP! please see picture***

Answer 1

Answer:

  14.  12/13 -8/13i

  15.  5

Step-by-step explanation:

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

$=\dfrac{0-4i}{2-3i}=\dfrac{-4i(2+3i)}{(2-3i)(2+3i)}=\dfrac{-8i-12i^2}{2^2-(3i)^2}\\\\=\dfrac{12-8i}{4+9}=\dfrac{12}{13}-\dfrac{8}{13}i$

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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).