Consider the complex valued function $$f\left( z \right) = 2{z^3} + b{\left| z \right|^3}$$ where $$z$$ is a complex variable. The value of $$b$$ for which the function $$f(z)$$ is analytic is __________.

An 8 Kbyte ROM with an active low Chip Select input CS is to be used in an 8085 microprocessor based system. The ROM should occupy the address range 1000H to 2FFFH. Theaddress lines are designated as A15 to A0, where A15is the most significant address bit.Which one of the following logicexpressions will generate the correct $$\overline{CS}$$ signal for this ROM?

The figure shows an $$RLC$$ circuit with a sinusoidal current source.

At response, the ratio $$\left| {{{\rm I}_L}} \right|/\left| {{{\rm I}_R}} \right|$$, i.e., the ratio of the magnitudes of the inductor current phasor and the resistor current phasor, is _________.

The switch S in the circuit shown has been closed for a long time. It is opened at time t = 0 and remains open after that. Assume that the diode has zero reverse current and zero forward voltage drop. The steady state magnitude of the capacitor voltage V_C (in volts) is ____________.