Question

A complex number zy has a magnitude 1211 = 2 and an angle 01 = 39º.-Express z, in rectangular form, as 21 = a + bi.Round a and b to the nearest thousandth.21+Show Calculator

Answer 1

a = 1.554

b = 1.258

`Z_1\text{ = }1.554\text{ + 1.258 i}`

Step-by-step explanation

Step 1: Given that:

`\text{ The absolute value or the modulus (r) = }|z_1|\text{ = 2}`
`\text{The argument of the complex number (}\theta)=39^0`

Step 2: The rectangular form of a complex number is given by:

`Z_1\text{ = a + bi}`

Step 3: Using basic trigonometric ratios to determine a and b

`\begin{gathered} \sin \text{ 39 = }(b)/(2) \\ b\text{ = 2 sin 39 = 1.258} \end{gathered}`
`\begin{gathered} \cos \text{ 39 = }(a)/(2) \\ a\text{ = 2 cos 39 = 1.554} \end{gathered}`

Hence, the rectangular form of the complex number is:

`Z_1\text{ = }1.554\text{ + 1.258i}`