Final answer:
To convert the complex number z = 6.4(cos51.34 + isin51.34) to its standard form a + bi, calculate a = 6.4 cos(51.34) and b = 6.4 sin(51.34), then combine them to form a + bi.
Step-by-step explanation:
The student has asked how to write the standard form of the complex number z = 6.4(cos51.34 + isin51.34). The standard form of a complex number is expressed as z = a + bi, where a is the real part and bi is the imaginary part, with i being the imaginary unit.
To convert from the trigonometric form to the standard form, use the following equations: a = r cos(\theta) and b = r sin(\theta). For this complex number, r = 6.4 and \theta = 51.34\u00B0. We calculate the real part a = 6.4 cos(51.34) and the imaginary part b = 6.4 sin(51.34).
After finding the cosine and sine values for 51.34 degrees, we multiply these by 6.4 to get a and b, respectively. This will give us z in the standard form a + bi.