Bissoy.com
Doctors Medicines MCQs Q&A

Square roots of −i , where i = √−1, are

Square roots of −i , where i = √−1, are Correct Answer <span class="math-tex">\(cos\left(-\frac{\pi}{4}\right)+i\:sin\left(-\frac{\pi}{4}\right), cos\left(\frac{3\pi}{4}\right)+i\:sin\left(\frac{3\pi}{4}\right)\)</span>

We know that,

i = eiπ/2

⇒ -i = e-iπ/2

⇒ √-i = ± 1/2 = ± e-iπ/4

= ±

= cos (π/4) - i sin (π/4);  - cos (π/4) + i sin (π/4)

= cos (-π/4) + i sin (-π/4);  cos (3π/4) + i sin (3π/4) 

Related Questions

Given below are three quantities named 1, 2 and 3. Based on the given information, you have to determine the relationship between the three quantities. You should use the given data and knowledge of Mathematics to choose between the possible answer. Quantity 1: Area of the innermost square. A square is made by joining the midpoints of a square of area 200 sq. m. The outermost square is called Square 1, The square inside it is called Square 2. The next square is made by joining midpoints of square 2 and is called Square 3. This process goes on. Square 5 is the innermost square. Quantity 2: A man starts with a speed of 10 km/hr. He increases his speed by 10 km/hr every hour at the start and drives at the same speed for that hour. If he traveled a total distance of 550 km. Find the time Quantity 3: Height of cylinder Its volume is equal to the volume of a cone whose radius is 14 cm and height is 39.3 cm. The radius of the cylinder is 14 cm
Given below are two statements, followed by four conclusions. Assume the facts in the statements to be true and decide which of the conclusions logically follow(s) from the statements. Statements: All roots are fruits. All fruits are guns. Conclusions: I. All roots are guns,. II. All guns are roots. III. All fruits are roots. IV. Some guns are roots.
Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements. Statements: All woods are roots. All fruits are roots. No woods are a fruit. Conclusion: (I) Some roots are fruits. (II) All roots are woods.
The length of each side of square A is increased by 100 percent to make square B. Again the length of each side of square B is increased by 50 percent to make square C. By what percent is the area of square C greater than the sum of the areas of square A and B?
Given below are two statements followed by conclusions. You have to take the given statements to be true even if they seem to be at variance with commonly known facts and then decide which of the given conclusions logically follow(s) from the given statements. Statements: I. Some flowers are fruits. II. All fruits are roots. Conclusions: I. All roots are fruits. II. Some roots are flowers.
In the formation of Routh-Hurwitz array for a polynomial, all the elements of a row have zero values. This premature termination of the array indicates the presence of 1. a pair of real roots with opposite sign 2. complex conjugate roots on the imaginary axis 3. a pair of complex conjugate roots with opposite real parts Which of the above statements are correct?
Three statements are given, followed by two conclusions numbered I, II  Assuming the statements to be true, even if they seem to be at variance with the commonly known facts, decide which of the following conclusions logically follow(s) from the statements. Statements: I. Some woods are roots. II. All fruits are roots III. No wood is fruit Conclusions: I. Some roots are fruits. II. No fruit is wood
Below a word is given in three sentences. Find out which one/ones make/makes a correct usage of the given word and mark the option accordingly. If the sentences are all correct mark option 5 as the answer. A: We were discussing the roots of the current economic malaise. B: Economic degradation roots in illiteracy.  C: The high crime rate has its roots in unemployment and poverty.
Given two quadratic equations, I. x2 - 31x + 240 = 0 Equation I has two roots x1, x2. (x1 > x2) II. 3y2 – 7y – 3 = 8y - 3y2 - 9 Equation II has two roots y1, y2. (y2 > y1) Find the equation whose roots are (– 2y1 + x1), - (y2 – x2).
Consider the following statements in respect of the roots of the equation x3 - 8 = 0: 1. The roots are non-collinear. 2. The roots lie on a circle of unit radius. Which of the above statements is/are correct?