Multiply \$z_1 = 7 + 4i\$ and \$z_2 = - 9 + 5i\$.

The given complex numbers

\$z_1 = 7 + 4i\$ and \$z_2 = - 9 + 5i\$

To multiply the complex numbers \$z_1 = 7 + 4i\$ and \$z 2 = - 9 + 5i\$, we use the distributive property as follows:
\$z_1. z_2 = (7 + 4i)(- 9 + 5i)\$.

Expanding this using distributive property and then simplify it:

\$7 times (- 9) + 7 times 5i + 4i times (- 9) + 4i times 5i\$

\$= - 63 + 35i - 36i + 20i^2\$

Since \$i^2 = - 1\$.

Substitute the \$i^2 = - 1\$ in the above expression and then simplify it:

\$= - 63 + 35i - 36i + 20(-1)^2\$

⇒ - 63 - 1i - 20

\$z_1. z_2 = - 83 - 1i\$

Therefore the multiply of \$z_1. z_2 = - 83 - 1i\$.

Option A, 38 - 2i, is incorrect because the real and imaginary parts do not match the calculated product

-38 - 2i

It is correct because it accurately performs the multiplication of complex numbers

-83 - 1i

(38 - 2i) is incorrect as it does not align with the calculated result of -83 - i

38 - 2i

This option has incorrect real and imaginary parts compared to the correct result of 83 - 1i, showing positive values instead of negative ones

83 +1i

Option

B

Can you summarize what you’ve understood in the above steps?