Complex Numbers

Question

-1

32

1

+1926

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

tomtom Feb 19, 2024

+1633

+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

proyaop · Answer 1 · 2024-02-19T05:29:03

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:

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