ANSWER
a = 1.554
b = 1.258
[tex]Z_1\text{ = }1.554\text{ + 1.258 i}[/tex]
EXPLANATION
Step 1: Given that:
[tex]\text{ The absolute value or the modulus (r) = }|z_1|\text{ = 2}[/tex][tex]\text{The argument of the complex number (}\theta)=39^0[/tex]
Step 2: The rectangular form of a complex number is given by:
[tex]Z_1\text{ = a + bi}[/tex]
Step 3: Using basic trigonometric ratios to determine a and b
[tex]\begin{gathered} \sin \text{ 39 = }\frac{b}{2} \\ b\text{ = 2 sin 39 = 1.258} \end{gathered}[/tex][tex]\begin{gathered} \cos \text{ 39 = }\frac{a}{2} \\ a\text{ = 2 cos 39 = 1.554} \end{gathered}[/tex]
Hence, the rectangular form of the complex number is:
[tex]Z_1\text{ = }1.554\text{ + 1.258i}[/tex]
