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Class 9 Math Real and Complex Numbers 1. Perform the indicated operations of the following complex numbers.(iii) \left(2 x y 5 y^{2}\right)-\left(\frac{1}{2} x y 6 y^{2}\right)


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1. Perform the indicated operations of the following complex numbers.(iii) \left(2 x y 5 y^{2}\right)-\left(\frac{1}{2} x y 6 y^{2}\right)

1. Identify the following statements as true or false.(vi) If (a-1)-(b+3) i=5+8 i then a=6 and b=-11
1. Identify the following statements as true or false.(vi) If  (a-1)-(b+3) i=5+8 i  then  a=6  and  b=-11

1. Identify the following statements as true or false.(vi) If (a-1)-(b+3) i=5+8 i then a=6 and b=-11

4. Verify that (\overline{\bar{z}})=z for the following complex numbers.(v) -2-3\left(-\frac{10}{9}\right) i
4. Verify that  (\overline{\bar{z}})=z  for the following complex numbers.(v)  -2-3\left(-\frac{10}{9}\right) i

4. Verify that (\overline{\bar{z}})=z for the following complex numbers.(v) -2-3\left(-\frac{10}{9}\right) i

1. Fill in the blanks.(viii) The conjugate of -3+5 i is
1. Fill in the blanks.(viii) The conjugate of  -3+5 i  is

1. Fill in the blanks.(viii) The conjugate of -3+5 i is

1. Perform the indicated operations of the following complex numbers.(i) (32)+(93)
1. Perform the indicated operations of the following complex numbers.(i)  (32)+(93)

1. Perform the indicated operations of the following complex numbers.(i) (32)+(93)

2. Simplify using law of exponent:(xi) \frac{3}{5} r^{3} s^{2} r^{7} r^{2} s^{2}
2. Simplify using law of exponent:(xi)  \frac{3}{5} r^{3} s^{2} r^{7} r^{2} s^{2}

2. Simplify using law of exponent:(xi) \frac{3}{5} r^{3} s^{2} r^{7} r^{2} s^{2}

2. Simplify using law of exponent:(iv) \left(-3 \times 5^{2}\right)^{3}
2. Simplify using law of exponent:(iv)  \left(-3 \times 5^{2}\right)^{3}

2. Simplify using law of exponent:(iv) \left(-3 \times 5^{2}\right)^{3}

1. Recognize the properties of real numbers used in the following:(viii) \frac{2}{11} \times \frac{11}{2}=\frac{11}{2} \times \frac{2}{11}=1
1. Recognize the properties of real numbers used in the following:(viii)  \frac{2}{11} \times \frac{11}{2}=\frac{11}{2} \times \frac{2}{11}=1

1. Recognize the properties of real numbers used in the following:(viii) \frac{2}{11} \times \frac{11}{2}=\frac{11}{2} \times \frac{2}{11}=1

1. Perform the indicated operations of the following complex numbers.(vii) (4-5)(5-4)
1. Perform the indicated operations of the following complex numbers.(vii)  (4-5)(5-4)

1. Perform the indicated operations of the following complex numbers.(vii) (4-5)(5-4)

1. Recognize the properties of real numbers used in the following:(x) \left(\frac{a}{b}\right) \times\left(\frac{b}{a}\right)=\left(\frac{b}{a}\right) \times\left(\frac{a}{b}\right)=1
1. Recognize the properties of real numbers used in the following:(x)  \left(\frac{a}{b}\right) \times\left(\frac{b}{a}\right)=\left(\frac{b}{a}\right) \times\left(\frac{a}{b}\right)=1

1. Recognize the properties of real numbers used in the following:(x) \left(\frac{a}{b}\right) \times\left(\frac{b}{a}\right)=\left(\frac{b}{a}\right) \times\left(\frac{a}{b}\right)=1

2. Write the conjugate of the following numbers.(i) 2+3 i
2. Write the conjugate of the following numbers.(i)  2+3 i

2. Write the conjugate of the following numbers.(i) 2+3 i

1. Perform the indicated operations of the following complex numbers.(iii) \left(2 x y 5 y^{2}\right)-\left(\frac{1}{2} x y 6 y^{2}\right)
1. Perform the indicated operations of the following complex numbers.(iii)  \left(2 x y 5 y^{2}\right)-\left(\frac{1}{2} x y 6 y^{2}\right)
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1. Perform the indicated operations of the following complex numbers.(iii) \left(2 x y 5 y^{2}\right)-\left(\frac{1}{2} x y 6 y^{2}\right)

4. Simplify and write your answer in the form a+b i .(vi) \frac{1}{(2+3 i)(1-i)}
4. Simplify and write your answer in the form  a+b i .(vi)  \frac{1}{(2+3 i)(1-i)}

4. Simplify and write your answer in the form a+b i .(vi) \frac{1}{(2+3 i)(1-i)}

3. Simplify and write your answer in form of a+i b (iii) \frac{2-6 i}{3-i}-\frac{4+i}{3+i}
3. Simplify and write your answer in form of  a+i b (iii)  \frac{2-6 i}{3-i}-\frac{4+i}{3+i}

3. Simplify and write your answer in form of a+i b (iii) \frac{2-6 i}{3-i}-\frac{4+i}{3+i}

3. Simplify using the law of exponent:(viii) \left\{\left(m m^{2} m^{3} m^{4}\right)^{2}\right\}^{5}
3. Simplify using the law of exponent:(viii)  \left\{\left(m m^{2} m^{3} m^{4}\right)^{2}\right\}^{5}

3. Simplify using the law of exponent:(viii) \left\{\left(m m^{2} m^{3} m^{4}\right)^{2}\right\}^{5}

5. Find the values of x and y when(iii) y^{2}+\frac{x}{3} i=121-\frac{9}{5} i
5. Find the values of  x  and  y  when(iii)  y^{2}+\frac{x}{3} i=121-\frac{9}{5} i

5. Find the values of x and y when(iii) y^{2}+\frac{x}{3} i=121-\frac{9}{5} i

3. Transform the following into exponential forms.(i) \sqrt{\left(\frac{3}{4}\right)}
3. Transform the following into exponential forms.(i)  \sqrt{\left(\frac{3}{4}\right)}

3. Transform the following into exponential forms.(i) \sqrt{\left(\frac{3}{4}\right)}

3. Simplifv using the law of exponent:(iv) \left\{(-3)^{3}(-4)^{2}\right\}^{3}
3. Simplifv using the law of exponent:(iv)  \left\{(-3)^{3}(-4)^{2}\right\}^{3}

3. Simplifv using the law of exponent:(iv) \left\{(-3)^{3}(-4)^{2}\right\}^{3}

2. Fill the correct real number in the following to make the real numbers property correct.(v) (-2) \neq(\square-n
2. Fill the correct real number in the following to make the real numbers property correct.(v)  (-2) \neq(\square-n

2. Fill the correct real number in the following to make the real numbers property correct.(v) (-2) \neq(\square-n

4. Represent the following numbers on the number line.(v) 2 \frac{3}{4}
4. Represent the following numbers on the number line.(v)  2 \frac{3}{4}
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4. Represent the following numbers on the number line.(v) 2 \frac{3}{4}

2. Fill the correct real number in the following to make the real numbers property correct.(iv) \left(\frac{59}{95}\right) \times\left(\frac{95}{59}\right)=\square
2. Fill the correct real number in the following to make the real numbers property correct.(iv)  \left(\frac{59}{95}\right) \times\left(\frac{95}{59}\right)=\square
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2. Fill the correct real number in the following to make the real numbers property correct.(iv) \left(\frac{59}{95}\right) \times\left(\frac{95}{59}\right)=\square

Example 02Show the following non terminating recurring decimal fractions on number linei. \frac{11}{6} ii. -\frac{5}{3}
Example 02Show the following non terminating recurring decimal fractions on number linei.  \frac{11}{6} ii.  -\frac{5}{3}
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Example 02Show the following non terminating recurring decimal fractions on number linei. \frac{11}{6} ii. -\frac{5}{3}

3. Find the conjugate of the following complex numbers.(iv) 1-i
3. Find the conjugate of the following complex numbers.(iv)  1-i
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3. Find the conjugate of the following complex numbers.(iv) 1-i

1. Fill in the blanks.(vi) \pi is a number.
1. Fill in the blanks.(vi)  \pi  is a number.
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1. Fill in the blanks.(vi) \pi is a number.

3. Represent the following rational numbers on number line.(ii) -\frac{8}{10}
3. Represent the following rational numbers on number line.(ii)  -\frac{8}{10}
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3. Represent the following rational numbers on number line.(ii) -\frac{8}{10}

1. Simplify the following:(ii) \frac{2^{4} \cdot 5^{3}}{10^{2}}
1. Simplify the following:(ii)  \frac{2^{4} \cdot 5^{3}}{10^{2}}
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1. Simplify the following:(ii) \frac{2^{4} \cdot 5^{3}}{10^{2}}

1. Fill in the blanks.(vii) \frac{22}{7} is a number.
1. Fill in the blanks.(vii)  \frac{22}{7}  is a number.
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1. Fill in the blanks.(vii) \frac{22}{7} is a number.

1. Simplify the following:(iii) \frac{(a+b)^{2} \cdot(c+d)^{3}}{(a+b) \cdot(c+d)^{2}}
1. Simplify the following:(iii)  \frac{(a+b)^{2} \cdot(c+d)^{3}}{(a+b) \cdot(c+d)^{2}}
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1. Simplify the following:(iii) \frac{(a+b)^{2} \cdot(c+d)^{3}}{(a+b) \cdot(c+d)^{2}}

Example 1Write each radical expression in exponential notation and each exponential expression in radical notation. Do not simplify.(ii) \sqrt[3]{x^{5}}
Example 1Write each radical expression in exponential notation and each exponential expression in radical notation. Do not simplify.(ii)  \sqrt[3]{x^{5}}
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Example 1Write each radical expression in exponential notation and each exponential expression in radical notation. Do not simplify.(ii) \sqrt[3]{x^{5}}

5. Find the additive and multiplicative inverse of the following real numbers.(vi) 0
5. Find the additive and multiplicative inverse of the following real numbers.(vi) 0
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5. Find the additive and multiplicative inverse of the following real numbers.(vi) 0

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