Find the product and write the result in standard form.
-$$( 5 + i ) ^ { 2 } - ( 6 - i ) ^ { 2 }$$
A) $- 11 + 22 \mathrm { i }$
B) $11 + 22 i$
C) $- 33$
D) $- 11 - 22 \mathrm { i }$ Complex numbers are used in electronics to describe the current in an electric circuit. Ohm's law relates the current in a circuit, I, in amperes, the voltage of the circuit, E, in volts, and the resistance of the circuit, R, in ohms, by the formula E = IR.

Question

Quizplus · Accepted Answer

First, expand both squares: $(5+i)^2 = 25 + 10i + i^2 = 24 + 10i$ (since $i^2 = -1$), and $(6-i)^2 = 36 - 12i + i^2 = 35 - 12i$. Subtracting the second from the first gives $24 + 10i - (35 - 12i) = -11 + 22i$.

Find the Product and Write the Result in Standard Form (5+i)2−(6−i)2( 5 + i ) ^ { 2 } - ( 6 - i ) ^ { 2 }(5+i)2−(6−i)2

Find the Product and Write the Result in Standard Form $( 5 + i ) ^ { 2 } - ( 6 - i ) ^ { 2 }$