Question

Write the following expression in standard form a + bi.

zz, where z = 4 - 6i
a) 4i - 6
b) -24 + 4i
c) 4 - 6i
d) -6i + 4

Answer 1

To write the expression zz in standard form a + bi, we substitute the value of z into the expression. By using the FOIL method, we can expand the expression and simplify it to obtain the standard form -20 - 48i.

Step-by-step explanation:

To write the expression zz in standard form a + bi, we substitute the value of z into the expression. In this case, z = 4 - 6i. So, the expression becomes (4 - 6i)(4 - 6i).

We can expand this expression using the FOIL method:

(4 - 6i)(4 - 6i) = 16 - 24i - 24i + 36i²

Next, we can simplify the expression by combining like terms:

16 - 24i - 24i + 36i² = 16 - 48i + 36i²

The imaginary unit i is defined as i² = -1. So, i² = -1. Substituting this value into the expression, we get:

16 - 48i + 36(-1) = 16 - 48i - 36 = -20 - 48i

Therefore, the expression zz in standard form a + bi is -20 - 48i.