Interpreting nonstandard trigonometric forms

In the preceding Conversion of forms question, parts \((ii)\) and \((iii)\) are not yet written in the standard form \(r(\cos\theta+i\sin\theta)\), with \(r>0\) and the same angle in both trigonometric terms.

Evaluate the real and imaginary components first. Determine the modulus and argument from those coordinates, using an Argand diagram to check the quadrant; do not read the argument directly from the displayed trigonometric angles.