Question

multiply the complex numbers (4 - 6i) and (8 - 5i).
a 2 + 68i
b 2 - 68i
c 62 - 28i
d 62 + 28i

Explanation:

Step1: Recall complex multiplication rule

To multiply complex numbers \((a + bi)\) and \((c + di)\), use the formula \((a + bi)(c + di)=ac + adi + bci + bdi^2\), and since \(i^2=-1\), it simplifies to \((ac - bd)+(ad + bc)i\). Here, \(a = 4\), \(b=-6\), \(c = 8\), \(d=-5\).

Step2: Calculate real part

Real part: \(ac - bd=(4\times8)-((-6)\times(-5)) = 32 - 30=2\).

Step3: Calculate imaginary part

Imaginary part: \(ad + bc=(4\times(-5))+((-6)\times8)=-20 - 48=-68\).

Step4: Form the complex number

Combine real and imaginary parts: \(2-68i\).

Answer:

B. \(2 - 68i\)