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avatar+1791 

Express $\frac{15 - 16i}{2 - 3i - 5 + 7i}$ in standard form.

 Feb 19, 2024

Best Answer 

 #1
avatar+1622 
+2

Combine like terms: \({15 - 16i\over{-3+4i}}\)

Rationalize the denominator by multiplying by conjugate to get difference of squares which removes the imaginary term:

\({(15 - 16i)(-3 - 4i)\over{(-3 + 4i)(-3-4i)}}={-45+48i-60i+64i^2\over{9-16i^2}}={19-12i\over25}={19\over25}-{12\over25}i\)

 Feb 19, 2024
 #1
avatar+1622 
+2
Best Answer

Combine like terms: \({15 - 16i\over{-3+4i}}\)

Rationalize the denominator by multiplying by conjugate to get difference of squares which removes the imaginary term:

\({(15 - 16i)(-3 - 4i)\over{(-3 + 4i)(-3-4i)}}={-45+48i-60i+64i^2\over{9-16i^2}}={19-12i\over25}={19\over25}-{12\over25}i\)

proyaop Feb 19, 2024

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