Solve the given problems. Refer to Example 4.

If E = 85 + 74j volts and Z = 2500 − 1200j ohms, find the complex-number representation for I.

Data from Example 4

In an alternating-current circuit, the voltage E is given by E = IZ, where I is the current (in A) and Z is the impedance (inΩ). Each of these can be represented by complex numbers. Find the complex number representation for I if E = 4.20 − 3.00j volts and Z = 5.30 + 2.65j ohms.
Because I = E/Z , we have

I = 4.20 - 3.00j 5.30 + 2.65j 22.26 - 11.13j (4.20 (5.30 + 2.65j)(5.30 14.31 - 27.03j 35.11 3.00j)(5.30 - 2.65j) 2.65j) 22.26 7.95 27.03j 5.30 +2.65 5.30 - 2.65 j = 15.90j + 7.95j 0.408 0.770j amperes multiply by conjugate of denominator