Final answer:
In complex numbers, multiplication involves multiplying the real and imaginary parts separately and combining them. The modulus of a complex number can be found using the formula: |a + ib| = sqrt(a^2 + b^2). The conjugate of a complex number a + ib is obtained by changing the sign of the imaginary part.
Step-by-step explanation:
In complex numbers, multiplication involves multiplying the real and imaginary parts separately and combining them. To find the modulus of a complex number, you can use the formula: |a + ib| = sqrt(a^2 + b^2), where a and b are the real and imaginary parts respectively. The conjugate of a complex number a + ib is obtained by changing the sign of the imaginary part, so the conjugate of a + ib is a - ib.
For example, if you have the complex numbers 2 + 3i and 5 - 4i, you can multiply them by multiplying the real and imaginary parts:
(2 + 3i)(5 - 4i) = (2*5 - 3*4) + (2*(-4) + 3*5)i = 10 - 12i - 8 + 15i = 2 + 3i.When multiplying imaginary numbers, you can simplify the products of i^n, where n is an integer, by using the pattern: i^0 = 1, i^1 = i, i^2 = -1, i^3 = -i.