1
MHT CET 2023 9th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $$Z_1=2+i$$ and $$Z_2=3-4 i$$ and $$\frac{\overline{Z_1}}{Z_2}=a+b i$$, then the value of $$-7 a+b$$ is (where $$i=\sqrt{-1}$$ and $$a, b \in R)$$

A
1
B
$$-$$1
C
$$\frac{-3}{25}$$
D
$$\frac{-9}{25}$$
2
MHT CET 2023 9th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $$Z_1=4 i^{40}-5 i^{35}+6 i^{17}+2, Z_2=-1+i$$, where $$i=\sqrt{-1}$$, then $$\left|Z_1+Z_2\right|=$$

A
5
B
13
C
12
D
15
3
MHT CET 2021 21th September Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $$z(2-i)=(3+i)$$, then $$z^{38}=$$, ( where $$z=x+i y$$)

A
$$-\left(2^{19}\right) \mathrm{i}$$
B
$$2^{19}$$ i
C
$$-\left(2^{19}\right)$$
D
$$2^{19}$$
4
MHT CET 2021 21th September Morning Shift
MCQ (Single Correct Answer)
+2
-0

The complex number with argument $$\frac{5 \pi^{\mathrm{c}}}{6}$$ at a distance of 2 units from the origin is

A
$$\sqrt{3}-\mathrm{i}$$
B
$$\sqrt{3}+\mathrm{i}$$
C
$$-\sqrt{3}-\mathrm{i}$$
D
$$-\sqrt{3}+\mathrm{i}$$
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