1) Simplify: \(\large\frac{5i^3}{7-4i}\)
2) Simplify \((5i^{12})(-2i)^3\)
3) Simplify \(i^{4721}\)
4) Find the value of \( \|z\| \) when \(z=7-3i\)
5) Simplify: \(\left|\left(3+2i\right)\left(-1+4i\right)\right|\)
6) Solve for \(z\): \(5i-\frac{2}{3}z=\left(4+i\right)\left(3-2i\right)\)
7) Simplify: \(\large\frac{\left(-2i+3+5i\right)\left(4-5i+2i^2\right)}{3+i}\)
8) Simplify: \( i^{4n +3} \) where \(n \in \mathbb{Z} \)
9) A monic quadratic polynomial, \( p(x) \), has real coefficients and a root \(4-3 i \). Determine \( p(x) \).
Solution Bank
2) Simplify \((5i^{12})(-2i)^3\)
3) Simplify \(i^{4721}\)
4) Find the value of \( \|z\| \) when \(z=7-3i\)
5) Simplify: \(\left|\left(3+2i\right)\left(-1+4i\right)\right|\)
6) Solve for \(z\): \(5i-\frac{2}{3}z=\left(4+i\right)\left(3-2i\right)\)
7) Simplify: \(\large\frac{\left(-2i+3+5i\right)\left(4-5i+2i^2\right)}{3+i}\)
8) Simplify: \( i^{4n +3} \) where \(n \in \mathbb{Z} \)
9) A monic quadratic polynomial, \( p(x) \), has real coefficients and a root \(4-3 i \). Determine \( p(x) \).
Solution Bank