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# Class 9 Math Real and Complex Numbers

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

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

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

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)

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

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}

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