MTH100 Practice Questions Lectures 1-22

Practice questions Lecture 1 to 5

Q1. Write the following expression in the form of a

ib

i i − , 4 10 i i

Solution

a) 3 i i

In order to simplify the above fraction, we will multiply and divide it by the conjugate of its denominator

( 1) ( 1) i i i i i i

i i

b) Part two will be done in the similar way. The simplified form will be 1( 17 59 ) i

Q2. z

i

then find

z z

Solution

( 5 8 ) z i z i z z i i i i i

Q3. If

z i

then find

.z z

Solution

2. 9, A x x x is even 3. 10} A x x N x

Solution

A {2,4,6,8,10}

A Empty set

A {2,3,4,5,6,7,8,9,10}

Q7. Let A be the set of all even numbers.

Let B be the set of all Number less than 100.

Is A a subset of B? or

Is B a subset of A?

Solution

Neither A is a subset of B nor B is a subset of A.

Q8. The complex numbers Z is given by

i Z i

Find modulus of Z .

Solution

i Z i

In order to find its modulus, we will first simplify it in the form of a+ib, for that we know that we are to multiply and divide it by the conjugate of denominator

i i i i i i i i

Now, we can find its absolute value or modulus as given below.

Z i

Q9. Evaluate

1. (2 )(3 i i
2. (4 5 )( 2 2 ) i i

Find z z z z , z z

Solution

i) z z z z z z i

ii) z z z z z z i

Q12. Evaluate

i. i i

ii. i i

iii. i i

Solution

As is taught in the previous question, before finding the modulus, we will first simplify the expression in to the form of a+ i b and it will be done by multiply and dividing the given fraction by the conjugate of denominator.

i) 2 (1 4i) i i

ii) 1 (18 13i) i i

Q13. i.

f x x

ii. f x x

iii. f x x iv. f x x