2025優(yōu)化設(shè)計(jì)一輪課時(shí)規(guī)范練53　復(fù)數(shù)

課時(shí)規(guī)范練53復(fù)數(shù)高考總復(fù)習(xí)優(yōu)化設(shè)計(jì)GAOKAOZONGFUXIYOUHUASHEJI202512345678910111213141516基礎(chǔ)鞏固練1.(2024·廣東廣州模擬)若a為實(shí)數(shù),且

=2-i,則a=(

)A.2 B.1C.-1 D.-2C解析

由題意得7+ai=(2-i)(3+i)=7-i,由復(fù)數(shù)相等得a=-1.12345678910111213141516A.1-2i B.1+2i C.2-i D.2+iB123456789101112131415163.(2024·江蘇蘇錫常鎮(zhèn)模擬)若復(fù)數(shù)z滿足(1-i)z=i,則復(fù)數(shù)z在復(fù)平面內(nèi)對(duì)應(yīng)的點(diǎn)所在的象限為(

)A.第一象限 B.第二象限C.第三象限 D.第四象限B12345678910111213141516D123456789101112131415165.(2024·河北邯鄲模擬)已知復(fù)數(shù)z是方程x2+4x+5=0的一個(gè)根,且復(fù)數(shù)z在復(fù)平面內(nèi)對(duì)應(yīng)的點(diǎn)位于第三象限,則

=(

)A.2-i B.2+iC.-2-i D.-2+i解析

復(fù)數(shù)范圍內(nèi)方程x2+4x+5=0的根為x=-2±i,因?yàn)閺?fù)數(shù)z在復(fù)平面內(nèi)對(duì)應(yīng)的點(diǎn)位于第三象限,所以z=-2-i,則

=-2+i.D123456789101112131415166.(2024·河北張家口模擬)已知i為虛數(shù)單位,若

為實(shí)數(shù),則實(shí)數(shù)a=(

)A.-2 B.4

C.2

D.-2B123456789101112131415167.復(fù)數(shù)z滿足|z-i|=,z在復(fù)平面內(nèi)對(duì)應(yīng)的點(diǎn)為(x,y),則(

)A.(x-1)2+y2=4 B.(x-1)2+y2=2C.x2+(y-1)2=4 D.x2+(y-1)2=2D解析

由復(fù)數(shù)的幾何意義知,z在復(fù)平面內(nèi)對(duì)應(yīng)點(diǎn)的軌跡是以(0,1)為圓心,以

為半徑的圓,則x,y滿足的方程為x2+(y-1)2=2.123456789101112131415168.(2024·河北滄州模擬)若兩個(gè)復(fù)數(shù)的實(shí)部相等或虛部相等,則稱這兩個(gè)復(fù)數(shù)為同部復(fù)數(shù).已知z=(1-i)3,則下列復(fù)數(shù)是z的同部復(fù)數(shù)的是(

)A.2+i B.3-2iC.4-i D.-3+2iB解析

由于z=(1-i)2(1-i)=-2i(1-i)=-2-2i,其實(shí)部和虛部均為-2,而3-2i與z的虛部相等,其余選項(xiàng)均不符合題意,所以3-2i是z的同部復(fù)數(shù).12345678910111213141516C12345678910111213141516ACD1234567891011121314151611.(2024·浙江紹興模擬)已知a,b∈R,若1+i是關(guān)于x的實(shí)系數(shù)方程x2+ax+b=0的一個(gè)根,其中i是虛數(shù)單位,則a+b=

.

01234567891011121314151612.(2024·遼寧遼陽(yáng)模擬)寫出一個(gè)滿足下列兩個(gè)條件的復(fù)數(shù)z=

.①z2的實(shí)部為5;②z的虛部不為0.3+2i(答案不唯一)解析

設(shè)z=a+bi(a,b∈R),則z2=a2-b2+2abi,依題意可得a2-b2=5,b≠0.故可取a=3,b=2,z=3+2i.12345678910111213141516綜合提升練D12345678910111213141516A1234567891011121314151615.(多選題)(2024·江蘇七市模擬)設(shè)z為復(fù)數(shù)(i為虛數(shù)單位),下列說(shuō)法正確的有(

)A.若z∈R,則z=

B.若z2∈R,則z∈RC.若z2+1=0,則z=i D.若(1+i)z=1-i,則|z|=1AD1234567891011121314151616.(多選題)(2024·山東青島模擬)關(guān)于x的方程x2=-4的復(fù)數(shù)解為z1,z2,則(

)A.z1z2=-4B.z1與z2互為共軛復(fù)數(shù)C.若z1=2