Question: If z = 2(cos(Ο/3) + i sin(Ο/3)), find z in rectangular form.
Options:
1 + β3i
2 + β3i
1 + 2i
2 + 2i
Correct Answer: 1 + β3i
Solution:
z = 2(1/2 + iβ3/2) = 1 + β3i.
If z = 2(cos(Ο/3) + i sin(Ο/3)), find z in rectangular form.
Practice Questions
Q1
If z = 2(cos(Ο/3) + i sin(Ο/3)), find z in rectangular form.
1 + β3i
2 + β3i
1 + 2i
2 + 2i
Questions & Step-by-Step Solutions
If z = 2(cos(Ο/3) + i sin(Ο/3)), find z in rectangular form.
Step 1: Identify the given expression for z, which is z = 2(cos(Ο/3) + i sin(Ο/3)).
Step 2: Calculate cos(Ο/3). The value of cos(Ο/3) is 1/2.
Step 3: Calculate sin(Ο/3). The value of sin(Ο/3) is β3/2.
Step 4: Substitute the values of cos(Ο/3) and sin(Ο/3) into the expression for z: z = 2(1/2 + iβ3/2).
Step 5: Distribute the 2 into the expression: z = 2 * (1/2) + 2 * (iβ3/2).
Step 6: Simplify the expression: z = 1 + β3i.
Polar to Rectangular Conversion β The question tests the ability to convert a complex number from polar form (using cosine and sine) to rectangular form (a + bi).
Trigonometric Values β It requires knowledge of the trigonometric values of cosine and sine for common angles, specifically Ο/3.
Soulshift FeedbackΓ
On a scale of 0β10, how likely are you to recommend
The Soulshift Academy?
