152/MR00. problem / Math - Solved Math Problems

MR-152 / 152. problem

Determine the value of the expression below:

${(2 i)}^{2} + (- 2 i)^{4}$

Source: MathReference: Generic Math Textbook - 152.)

Algebra → Complex numbers → Exponentiation of complex numbers

${(2 i)}^{2} + (- 2 i)^{4}$

$= 2^{2} \cdot i^{2} + (- 2)^{4} \cdot i^{4}$

$= 4 \cdot (- 1) + 16 \cdot 1$

$= - 4 + 16$

$= 12$