# Mathematics Questions and Answers – Complex Numbers-2

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This set of Mathematics Question Bank focuses on “Complex Numbers-2”.

1. z1=1+2i and z2=2+3i. Find z1z2.
a) 2+6i
b) -4+0i
c) -4+7i
d) 8+7i

Explanation: z1z2 = (1+2i) (2+3i)
= 2 + 3i + 4i -6
= -4 + 7i.

2. i2 =______________________
a) 1
b) -1
c) i
d) -i

Explanation: We know, i = $$\sqrt{-1}$$
=> i2 = -1.

3. i7 =______________
a) 1
b) -1
c) i
d) -i

Explanation: We know, i = $$\sqrt{-1}$$
=> i2 = -1 => i4 = 1.
So, i7 = i4.i3 = 1*i2*i = (-1)*i = -i.

4. i241 =________________
a) 1
b) -1
c) i
d) -i

Explanation: We know, i = $$\sqrt{-1}$$
=> i2 = -1 => i4 = 1.
So, i241 = (i4)60 * i = 1 * i = i.

5. Square roots of -7 are____________
a) 7i and -7i
b) $$\sqrt{7}$$ i
c) –$$\sqrt{7}$$ i
d) $$\sqrt{7}$$ i and –$$\sqrt{7}$$ i

Explanation: We know, i2 = -1.
-7 = 7(i2)
Square root of i2 is ±i so, square root of -7 are $$\sqrt{7}$$i and –$$\sqrt{7}$$i.

6. (-i) (8+5i) =________________
a) 8+5i
b) -8-5i
c) -5-8i
d) 5-8i

Explanation: (-i) (8+5i) = -8i – 5 i2
= -8i -5(-1) = 5-8i.

7. (2-i)3 =________________
a) 2-3i
b) 8-i
c) 2-11i
d) 2+11i

Explanation: We know, (a-b)3 = a3-b3-3ab(a-b)
So, (2-i)3 = 23-(i)3-3(2)(i) (2-i)
= 8-(-i)-6i(2-i)
= 8+i-12i-6
= 2-11i.

8. Is z*$$\bar{z}$$ = |z|2?
a) True
b) False

Explanation: Let z=a+ bi
=>$$\bar{z}$$ = a-bi
So, z*$$\bar{z}$$ = (a+bi) (a-bi) = a2-(bi)2 = a2-(b2) (-1) = a2+b2
|z|=$$\sqrt{a^2+b^2}$$ => |z|2 = a2+b2
Hence, z*$$\bar{z}$$ = |z|2.

9. Find multiplicative inverse of 3+5i.
a) 87+145i
b) 87-145i
c) 145-87i
d) 145+87i

Explanation: We know, z*$$\bar{z}$$ = |z|2.
(1/z) = $$\bar{z}$$|z|2
z-1=(3-5i) (32+52) = (3-5i) (29) = 87-145i.

10. i-35 =___________________
a) 1
b) -1
c) i
d) -i 