Express the complex number \((5i)\left(\dfrac{-3 - i}{5}\right)\) in the form \(a + ib\).
\(3 + i0\)
Simplify and express in the form \(a + ib\): \(i^9 + i^{19}\).
\(0 + i0\)
Express the value of \(i^{-39}\) in the form \(a + ib\).
0 + i1
Express \(3(7 + i7) + i(7 + i7)\) in the form \(a + ib\).
14 + 28i
Express \((1 - i) - (-1 + i6)\) in the form \(a + ib\).
2 - 7i
Express \(\left(\dfrac{1}{5} + i\dfrac{2}{5}\right) - \left(4 + i\dfrac{5}{2}\right)\) in the form \(a + ib\).
-\dfrac{19}{5} - \dfrac{21i}{10}
Express \(\left(\dfrac{1}{3} + i\dfrac{7}{3}\right) + \left(4 + i\dfrac{1}{3}\right) - \left(-\dfrac{4}{3} + i\right)\) in the form \(a + ib\).
\dfrac{17}{3} + i\dfrac{5}{3}
Find \((1 - i)^4\) and express it in the form \(a + ib\).
-4 + i0
Find \(\left(\dfrac{1}{3} + 3i\right)^3\) and express it in the form \(a + ib\).
-\dfrac{242}{27} - 26i
Find \(\left(-2 - \dfrac{1}{3}i\right)^3\) and express it in the form \(a + ib\).
-\dfrac{22}{3} - i\dfrac{107}{27}
Find the multiplicative inverse of the complex number \(4 - 3i\).
\dfrac{4}{25} + i\dfrac{3}{25}
Find the multiplicative inverse of the complex number \(\sqrt{5} + 3i\).
\dfrac{\sqrt{5}}{14} - i\dfrac{3}{14}
Find the multiplicative inverse of the complex number \(-i\).
0 + i1
Express the expression \(\dfrac{(3 + i\sqrt{5})(3 - i\sqrt{5})}{(\sqrt{3} + \sqrt{2}i)(\sqrt{3} - i\sqrt{2})}\) in the form \(a + ib\).
0 - i\dfrac{7\sqrt{2}}{2}