(3-4i) (3+4i)=a+ib হলে, ab = কত?

প্রশ্ন: \((3 - 4i)(3 + 4i) = a + ib\) হলে, \(ab\) কত?

সমাধান:

প্রথমে দুইটি সংকেতের গুণফল নির্ণয় করি:

\[
(3 - 4i)(3 + 4i) = 3 \times 3 + 3 \times 4i - 4i \times 3 - 4i \times 4i
\]

1. \(3 \times 3 = 9\)
2. \(3 \times 4i = 12i\)
3. \(-4i \times 3 = -12i\)
4. \(-4i \times 4i = -16i^2\)

\[
(3 - 4i)(3 + 4i) = 9 + 12i - 12i - 16i^2
\]

\[
= 9 + (12i - 12i) - 16i^2
\]

\[
= 9 - 16i^2
\]

\[
= 9 - 16 \times (-1) = 9 + 16 = 25
\]